MARKEY, Chief Judge.

Appeal from a judgment of the district court, Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., C.A. Nos. 4935 and G293-71 (W.D.Mich. Sept. 15, 1975), adopting, with an unpublished opinion, the report of the special master awarding plaintiff, as dam*1155ages for patent infringement, a reasonable royalty of 2 1 A%. We reverse and remand.

Litigation Background

In 1964 plaintiff Panduit Corp. (Panduit) sued defendant Stahlin Bros. Fibre Works, Inc. (Stahlin) for infringement of Panduit’s Walch patent No. 3,024,301, covering duct for wiring of electrical control systems. In 1969, the district court found claim 5 valid and infringed by the “Lok-Slot” and “Web-Slot” ducts made and sold by Stahlin, enjoined Stahlin from further infringement, and ordered an accounting. 298 F.Supp. 435, 162 USPQ 114 (W.D.Mich.1969). That judgment was affirmed on appeal. 430 F.2d 221,166 USPQ 524 (6th Cir. 1970), cert. denied, 401 U.S. 939, 91 S.Ct. 932, 28 L.Ed.2d 218, 168 USPQ 673 (1971).

Thereafter, the district court adjudged Stahlin in contempt of the court’s injunction, because of Stahlin’s making and selling the “Tear Drop” duct, a colorable imitation of the infringing “Lok-Slot,” 338 F.Supp. 1240, 172 USPQ 650 (W.D.Mich. 1972). That judgment was also affirmed on appeal. 476 F.2d 1286, 178 USPQ 12 (6th Cir. 1973).

In 1971, the district court appointed a master to determine Panduit’s damages pursuant to 35 U.S.C. § 284,1 to take evidence, and render a report on the issues of treble damages, interest, costs, and attorney fees. The district court, in adopting in toto the master’s report, considered the master’s findings of fact not clearly erroneous, and stated that “the Master had correctly applied the law to the circumstances of this case.” The report recommended $44,709.60 in damages, based on a royalty of 2V2% of gross sales price, the percentage being calculated on Stahlin’s testimony that its normal profit on all of its products was 4.04% and the concept that a “reasonable royalty” entailed some level of profit to the “licensee.” Horvath v. McCord Radiator and Mfg. Co., 100 F.2d 326 at 335, 40 USPQ 394 at 403 (6th Cir. 1938), cert. denied, 308 U.S. 581, 60 S.Ct. 101, 84 L.Ed. 486, 43 USPQ 520 (1939).

Fact Background

The duct manufactured by Panduit was invented by its president, Jack Caveney. Panduit began to make and sell the duct in 1955, and Caveney applied for a patent in 1956, In an interference proceeding in the Patent Office, it was determined that Walch, an employee of General Electric, was the first inventor of the duct. A patent issued to General Electric, as Walch’s assignee, on March 6, 1962. Panduit then acquired the Walch patent from General Electric and established a firm policy of exercising its right to that patent property, 1. e., of the right to exclude others from making and selling the patented duct.

Stahlin began to manufacture and sell the “Lok-Slot” and “Web-Slot” ducts in 1957, and continued to do so after issuance of the Walch patent and its sale to Panduit in 1962. On January 1, 1963, Stahlin introduced a price cut of approximately 30% on its “Lok-Slot” and “Web-Slot” ducts.

Panduit seeks $808,003 as damages for lost profits on lost sales over the period March 6, 1962, the date of first infringement, to August 7, 1970, the effective date of the initial injunction;2 or, alternatively, a 35% reasonable royalty rate yielding $625,940. In addition, Panduit seeks $4,069,000 in profits lost on Panduit’s own sales because of Stahlin’s price cut.

Issue

The dispositive issue is whether the master’s determination of a reasonable royalty was in error.

*1156OPINION

The statute, 35 U.S.C. § 284, requires that the patent owner receive from the infringer “damages adequate to compensate for the infringement.” In Aro Mfg. Co. v. Convertible Top Replacement Co., 377 U.S. 476 at 507, 84 S.Ct. 1526, 1543, 12 L.Ed.2d 457, 141 USPQ 681 at 694 (1964), the Supreme Court stated:

But the present statutory rule is that only “damages” may be recovered. These have been defined by this Court as “compensation for the pecuniary loss he [the patentee] has suffered from the infringement, without regard to the question whether the defendant has gained or lost by his unlawful acts.” Coupe v. Royer, 155 U.S. 565, 582, 15 S.Ct. 199, 39 L.Ed. 263. They have been said to constitute “the difference between his pecuniary condition after the infringement, and what his condition would have been if the infringement had not occurred.” Yale Lock Mfg. Co. v. Sargent, 117 U.S. 536, 552, 6 S.Ct. 934, 29 L.Ed. 954. The question to be asked in determining damages is “how much had the Patent Holder and Licensee suffered by the infringement. And that question [is] primarily: had the Infringer not infringed, what would Patent Holder-Licensee have made?” [Citing Livesay Window Co. v. Livesay Industries, Inc., 251 F.2d 469, 471, 116 USPQ 167, 168 (5th Cir., 1958).]

Panduit argues that the district court erred (1) in denying Panduit its lost profits due to lost sales, or, in the alternative, a 35% reasonable royalty; and (2) in denying Panduit its lost profits from its own actual sales due to Stahlin’s price cut.

Lost Profits Due to Lost Sales

To obtain as damages the profits on sales he would have made absent the infringement, i. e., the sales made by the infringer, a patent owner must prove: (1) demand for the patented product, (2) absence of acceptable noninfringing substitutes, (3). his manufacturing and marketing capability to exploit the demand, and (4) the amount of the profit he would have made. 3 R. White, Patent Litigation: Procedure and Tactics § 9.03[2]. See, e. g., Bros. Inc. v. W. E. Grace Mfg. Co., 320 F.2d 594 at 598, 138 USPQ 357 at 358 (5th Cir. 1963) and Electric Pipe Line, Inc. v. Fluid Systems, Inc., 250 F.2d 697, 116 USPQ 25 (2d Cir. 1957).

It is not disputed that Panduit established elements (1) and (3). Regarding (2), the master found that: “The evidence clearly shows the existence of acceptable non-infringing substitute ducts which would have permitted the defendant to retain its customers.” That finding, as discussed below, was in error. However, Pan-duit is not entitled to its lost profits on lost sales in this case because of its failure to establish element (4).

The district court upheld as not clearly erroneous the master’s finding that “there was insufficient evidence from which a fair determination could be made as to the amount of profit plaintiff would have made on such sales.”

Panduit’s Achilles heel on element (4) is a lack of evidence on its fixed costs. Panduit alleges that its omission is overcome by other evidence and by General Electric Co. v. Sciaky Bros., Inc., 415 F.2d 1068, 163 USPQ 257 (6th Cir. 1969). Sciaky is distinguishable and therefore not controlling on fixed costs. The accounting presented by Sciaky’s expert witnesses included some overhead expenses, but omitted others which those witnesses testified were general and “paid by Sciaky during the years in question and would not have been greater if these additional machines had been produced and sold by Sciaky.” 415 F.2d at 1075, 163 USPQ at 262. General Electric (the infringer) disputed that theory, but offered no testimony to contradict it. The court held:

Whether Sciaky’s accounting method was accurate or not was a matter to be decided on the basis of testimony in the hearing before the Master. This was the specific function of that hearing. We do not believe that this issue can properly be *1157decided as a matter of law before this court on appeal.

415 F.2d at 1075, 163 USPQ at 262.

In the present case, Stahlin did dispute Panduit’s accounting theory, presenting its own expert witnesses to contradict it. Under Sciaky, the accuracy of the patent owner’s accounting method is “a matter to be decided on the basis of testimony in the hearing before the Master.” The master here found, on the basis of the evidence before him, and the district court agreed, that Panduit’s accounting theory was deficient. As was said in Sciaky:

[WJhere the District Court adopts the Master’s findings of fact, Fed.R.Civ.P. 52(a) provides that such findings “shall be considered as the findings of the court” which cannot be set aside unless “clearly erroneous.”

415 F.2d at 1073, 163 USPQ at 260.

We realize, as noted in Sciaky, that Pan-duit’s theory is “by no means novel in patent damage cases.” 415 F.2d at 1075, 163 USPQ at .262. Nevertheless, there is no evidence of record sufficient to support a conclusion that the master’s findings respecting Panduit’s omission, whether of certain fixed costs or of certain variable costs, were clearly erroneous.3

Panduit’s argument that the master was required by Fed.R.Civ.P. 53(d)(3)4 to require a statement taking into account its omitted costs is without merit. The rule is discretionary, not mandatory, and it was not an abuse of the master’s discretion to refuse the requested statement.

On the issue of Panduit’s lost profits on lost sales, we affirm the district court.

Stahlin’s Price Cut

The district court upheld as not clearly erroneous the master’s finding that: “Any loss in [Panduit’s] profits due to the price reduction was more than compensated by the gain in profits due to the increase in plaintiff’s sales volume because of the price reduction. Thus, the price reduction resulted in a net increase in profit to the plaintiff.”

The right to damages caused by price reduction stands on the same ground as that to damages caused by lost sales. McSherry Mfg. Co. v. Dowagiac Mfg. Co., 163 F. 34 at 35 (6th Cir. 1908). Having accepted the master’s evaluation, that the testimony of Stahlin’s accounting and economic experts was more credible and persuasive than that of Panduit’s, we are bound, in the absence of clear evidence to the contrary, to accept as not clearly erroneous the master’s finding that the price reduction in this case produced a net increase in Panduit’s profits.

We affirm, therefore, the district court’s refusal to award damages on the basis of Stahlin’s price cut.

Reasonable Royalty

When actual damages, e. g., lost profits, cannot be proved, the patent owner is entitled to a reasonable royalty. 35 U.S.C. § 284. See also Enterprise Mfg. Co. v. Shakespeare Co., 141 F.2d 916 at 920, 61 USPQ 201 at 204 (6th Cir. 1944); Egry Register Co. v. Standard Register Co., 23 F.2d 438 at 442 (6th Cir. 1928); Wm. Bros Boiler and Mfg. Co. v. Gibson-Stewart Co., Inc., 312 F.2d 385 at 386, 136 USPQ 239 at 240 (6th Cir. 1963). A reasonable royalty is an amount “which a person, desiring to *1158manufacture and sell a patented article, as a business proposition, would be willing to pay as a royalty and yet be able to make and sell the patented article, in the market, at a reasonable profit.” Goodyear Tire and Rubber Co. v. Overman Cushion Tire Co., 95 F.2d 978 at 984, 37 USPQ 479 at 484 (6th Cir. 1937) (citing Rockwood v. General Fire Extinguisher Co., 37 F.2d 62 at 66, 4 USPQ 299 at 303 (2d Cir. 1930)), appeal dismissed on motion of counsel for petitioners, 306 U.S. 665, 59 S.Ct. 460, 83 L.Ed. 1061 (1938).

The key element in setting a reasonable royalty after determination of validity and infringement is the necessity for return to the date when the infringement began. In the present case, that date is March 6, 1962. On that date, Panduit possessed the particular property right found to have been infringed by Stahlin. On that date, Panduit had a particular profit margin, and the property right to exclude others from making, using, or selling the patented product. 35 U.S.C. § 271.5 At that point Stahlin chose to continue the making and selling of the patented product.

As a result of Stahlin’s election to infringe its property right, Panduit has suffered substantially. See United States Frumentum Co. v. Lauhoff, 216 F. 610 (6th Cir. 1917). Though unable to prove the actual amount of lost profits or to establish a damage figure resulting from Stahlin’s price cut, Panduit was clearly damaged by having been forced, against its will, to share sales of the patented product with Stahlin. Further, Panduit has been forced into thirteen years of expensive litigation, involving $400,000 in attorney fees, a trial, a contempt proceeding to enforce the court’s injunction, a hearing on damages, and three appeals. For all this, the “damages adequate to compensate for the infringement,” 35 U.S.C. § 284, have thus far been found to total $44,709.60.6

Having elected to continue the manufacture and sale of the patented duct after the patent issued, and having elected to manufacture and sell a second infringing product in the face of the court’s injunction, Stahlin was able to make infringing sales, as found by the master, totalling $1,788,384.

The setting of a reasonable royalty after infringement cannot be treated, as it was here, as the equivalent of ordinary royalty negotiations among truly “willing” patent owners and licensees. That view would constitute a pretense that the infringement never happened. It would also make an election to infringe a handy means for competitors to impose a “compulsory license” policy upon every patent owner.

Except for the limited risk that the patent owner, over years of litigation, might meet the heavy burden of proving the four elements required for recovery of lost profits, the infringer would have nothing to lose, and everything to gain if he could count on paying only the normal, routine royalty non-infringers might have paid. As said by this court in another context, the infringer would be in a “heads-I-win, tails-you-lose” position. Troxel Mfg. Co. v. Schwinn Bicycle Co., 465 F.2d 1253 at 1257, 175 USPQ 65 at 68 (6th Cir. 1972), cert. denied, 416 U.S. 939, 94 S.Ct. 1942, 40 L.Ed.2d 290 (1974).

On the date a patent issues, a competitor which made no investment in research and development of the invention, has four options: (1) it can make and sell a non-infringing substitute product, and refrain from making, using, or selling a prod*1159uct incorporating the patented invention; (2) it can make and sell the patented product, if the patent owner be willing, negotiating a license and paying a reasonable (negotiated) royalty; (3) it can simply take the invention, running the risk that litigation will ensue and that the patent will be found valid and infringed, or (4) it can take a license under option (2) and thereafter repudiate its contract, challenging the validity of the patent.7 Determination of a reasonable royalty, after election of option (3) , cannot, without injustice, be treated as though the infringer had elected option (2) in the first place.

Determination of a “reasonable royalty” after infringement, like many devices in the law, rests on a legal fiction. Created in an effort to “compensate” when profits are not provable, the “reasonable royalty” device conjures a “willing” licensor and licensee, who like Ghosts of Christmas Past, are dimly seen as “negotiating” a “license.” There is, of course, no actual willingness on either side, and no license to do anything, the infringer being normally enjoined, as is Stahlin, from further manufacture, use, or sale of the patented product.

The amount of a reasonable royalty after infringement turns on the facts of each case, as best they may be determined. Among the relevant facts are: “what plaintiff’s property was, to what extent defendant has taken it, its usefulness and commercial value as shown by its advantages over other things and by the extent of its use,” United States Frumentum, 216 F. at 617, and the commercial situation, Egry, 23 F.2d at 443.

In determining that a reasonable royalty rate here was 2V2%, the master found: (1) there were present in the market on the date of first infringement acceptable nonin-fringing substitutes and competing duct producers, (2) Panduit could not have maintained a high price differential in the face of competition from the substitute ducts, (3) on the hypothetical negotiation date, both Panduit and Stahlin would have been aware of the competitive state of the market, and of the probability of future price cuts, including Stahlin’s, (4) the testimony of Stah-lin’s patent law expert, Scofield, was “more credible and persuasive and more in line with the factual realities of this case” than the testimony of Panduit’s patent law expert, and (5) Stahlin’s profit on gross sales of all its products for the relevant period was 4.04%, and there was “no evidence to indicate that the profit on its duct sales was significantly higher than the profit on its total sales generally.” The district court held those findings not clearly erroneous. We disagree.

In adopting the master’s report, the district court stated:

The Master based his finding that non-infringing substitutes were available principally upon the additional finding that defendant was markedly successful in switching its customers to noninfringing products when that became necessary. The latter finding is not clearly erroneous, and although defendant was not actually selling the principal noninfringing substitute . . . during the relevant time period, it is not erroneous to conclude that the substitute was available. Cf. Hughes Tool Co. v. G. W. Mur *1160 phy Indus., Inc., 491 F.2d 923, 930-931 (5th Cir. 1973).

The district court also found the master correct in defining an acceptable nonin-fringing substitute as “a product which customers are willing to buy in place of the infringing product.”

In concluding that error occurred with respect to substitutes, we are mindful of the comments of this court in Enterprise Mfg., 141 F.2d at 920, 61 USPQ at 205:

The appellee, by infringing use, has paid tribute to the utility of the device infringed. As was said by Judge Hicken-looper for this court, in Seymour v. Ford Motor Company, 6 Cir., 44 F.2d 306, 308 [7 USPQ 182, 184]: “The patent is itself evidence of such utility, and the use of the patented device by the defendant has long been recognized as an admission of this fact, and as creating an estoppel upon the defendant to deny such utility. [Citing numerous cases.]”

There can be no doubt that, as found by the District Court, the substantial value of the Case patent was recognized by the infringer in its catalogues and other advertisements. The advantages proclaimed in these advertisements carry more forceful recognition of the value of the patent infringed than belated denial of its value rejects. Compare Cugley v. Bundy Incubator Company, 6 Cir., 93 F.2d 932, 934 [36 USPQ 524, 526].

Also pertinent are the comments of the court in Georgia-Pacific Corp. v. U.S. Plywood-Champion Papers, 318 F.Supp. 1116 at 1123, 166 USPQ 235 at 241 (S.D.N.Y.1970), aff’d 446 F.2d 295, 170 USPQ 369 (2d Cir. 1971), cert. denied, 404 U.S. 870, 92 S.Ct. 105, 30 L.Ed.2d 114 (1971):

Noteworthy is the fact that, despite the allegedly fierce competition between the Weldtex [the patented goods] and other decorative plywoods, GP [plaintiff-in-fringer] deliberately decided to duplicate Weldtex notwithstanding the caveat of GP’s own counsel that an expensive infringement suit was inevitable. GP’s calculated infringement of Weldtex is an admission by conduct that it regarded Weldtex as occupying a uniquely favorable position in the market. [Emphasis added.]

In the present case, the master’s finding that Panduit had competitors was not erroneous, but the implication drawn therefrom was. At the time the patent issued, there were four competitors, but they were recognized as making and selling not substitutes but infringing ducts. Competition between those selling infringing ducts was admittedly fierce. Infringer Stahlin, however, cannot expect to pay a lesser royalty, as compensation for its infringement, on the ground that it was not the only infringer. Cf. Bros Inc. v. W. E. Grace Mfg. Co., 320 F.2d at 598, 138 USPQ at 358-59 (patent owner awarded lost profits).

Illustrative of the absence of acceptable substitutes is Stahlin’s inability to avoid infringement, even if it had ever wanted to. Having begun manufacture of the duct in 1957, Stahlin continued after the patent issued in 1962, after Panduit instituted its infringement suit in 1964, and after the district court’s injunction in 1969.8

*1161At the time of the first injunction, virtually all of Stahlin’s sales of electrical duct were of the infringing type. Stahlin’s early-but-grudging recognition of the unique advantages of Panduit’s patented duet was evidenced by an intra-company memo. Dated June 21, 1957, it was issued in the earliest stages of Stahlin’s manufacture of the “Lok-Slot:”

It seems that some of our customers have preferred a full-slotted channel; one that permits slipping the wire in place rather than threading the end through an opening. It’s advantages are questionable but we always try to give our customers even more than they want. Thus, we have developed the Lok-Slot construction.

Lok-Slot construction is evident in the name. Like any slot, Lok-Slot permits easy entry of wires. Unlike any other slot, Lok-Slot keeps the wires from readily popping up all over the place while connections are being made. The reason is Lok-Slot’s slim throat construction which allows single wires in and out easily enough but “chokes up” on “mass exits.”

Using Panel Chanel with Lok-Slot construction, wires don’t have to be threaded through the channel openings. .

The Lok-Slot construction is not a cure-all. Frankly, it is not quite as easy to remove and put on the covers with this construction. In any event, there are some customers who prefer the full-slotted construction . . . and Lok-Slot is the best design approach yet to this form of channel.

In other words, don’t push this construction . . . but if there is customer preference in this direction, you have the best design to offer.

The district court opinion following the infringement trial recognized the same advantages over non-infringing ducts:

General Electric produced a steel grille which had perforated round roles through which wires were threaded (PX 63A). This device was patented in the 1930’s (PX 67-6A and PX 62, at 50-53). Another product in use in the early 1950’s was a U-shaped wiring duct (PX 2) which incorporated multiple openings in the side walls through which wires were threaded and then connected to the electrical components.

However, ducts with holes also had shortcomings. When these ducts were filled with wires, the wires were rather inaccessible añcl.it was difficult to trace individual wires or to revise the wiring. For example, to remove any wire from the duet, it was necessary to disconnect the wire and thread it back through the hole. If the wire was not near the top of the duct, it was frequently necessary to remove a number of wires to gain access to the wire being traced or rerouted. * * * *

Mr. Walch, in 1953 as a senior advance engineer at General Electric, was given a broad assignment to improve wiring practices, including the improvement of wiring duct design. Four desirable functions or results were stressed by Mr. Walch in his work on the design of an improved wiring duct:

(1) Easy insertion of wires in the duct;

(2) Prevention of accidental removal of wires from the duct;

*1162(3) Provision of maximum useful space for leading wires out of the duct; and

(4) Facilitation of intentional removal of wires from the duct.

298 F.Supp. at 437-38,162 USPQ at 116-17. That evaluation was affirmed on appeal by this court. 430 F.2d at 225, 166 USPQ at 525.

Proof of the absence of noninfringing substitutes:

[Ijnvolves some of the same evidence as that which was introduced in support of the validity of the patent. The patent owner who had proved a long-felt need for a particular invention has a lighter burden in establishing that his customers, as well as the infringer’s customers, were in fact seeking to obtain the patented solution to such need or problem. The other side of the coin involves a strong showing by the infringer that although the patent may have embodied some trifling improvement which was patentable to a narrow extent, such improvement did not create any preference for the patented product rather than a nonin-fringing substitute. .

3 R. White, § 9.03[2]. The prior district and appellate court opinions leave no doubt that the patented product filled a waiting need and met with commercial success due to its merits. Stahlin’s own intra-company memo (PX 58), and its $1,788,384 sales of infringing ducts during the period when allegedly acceptable noninfringing substitutes are now said to have been available, leave no doubt that the patented improvement created a substantial customer preference. A product lacking the advantages of that patented can hardly be termed a substitute “acceptable” to the customer who wants those advantages.9 The post-hoc circumstance that Stahlin, when finally forced to obey the court’s injunction, was successful in “switching” customers to a noninfringing product, does not destroy the advantage-recognition attributable to the patent over the prior 15 years. Those preferred advantages were recognized by Stahlin itself, by other infringers, by customers, by the district court, and by this court. That Stah-lin’s customers, no longer able to buy the patented product from Stahlin, were willing to buy something else from Stahlin, does not establish that there was on the market during the period of infringement a product which customers in general were, in the master’s words, “willing to buy in place of the infringing product.” Moreover, Stah-lin’s “switching” occurred years after the date on which the determination of available substitutes must focus, i. e., the date of first infringement.

Hence, the 2Va% royalty rate recommended by the master and adopted by the district court is clearly erroneous on its face, the master’s recommendation having been based in large part on erroneous finding (1), that there were “acceptable” noninfringing substitutes during the relevant period.

The master’s finding (2), that Panduit could not have maintained its high price differential (allegedly 30%) because of competition from substitutes, and his finding (3) that in March 1962 the parties were aware of the probability of a future price cut, must also fall. Evidence is lacking, as we have said, that acceptable substitutes were on the market on the focus-date of first infringement. For some five years after Stahlin began manufacture of its “Lok-Slot” duct, purchasers of the patented product were willing to pay a substantial differential. It was not until January 1, 1963, some nine months after the hypothetically “willing” licensor and licensee are supposed to have negotiated a royalty, that( Stahlin made its price cut. We find no evidence in the record to support the mas*1163ter’s supposition that the parties would have had that future price cut in mind in March 1962. On the contrary, the hypothesis is that Stahlin was a royalty-paying licensee on January 1, 1963, and nothing of record indicates an expectation that a licensee would cut its price or that any particular room existed to accommodate both a price cut and royalty payments.

Section 284 of the statute authorizes the use of experts in determining a reasonable royalty. However, the master’s reliance on Scofield’s testimony, and the district court’s acceptance thereof, were clearly erroneous. That testimony was in substantial conflict with case law established in this circuit and elsewhere. Scofield testified that a reasonable royalty could be equated to the average value of all negotiated royalties, which in his experience was “between 1 and 5 per cent of the net selling price of the products,”10 and concluded that a reasonable royalty in this case would be 2V2%. He specifically testified that his experience was in the negotiation of licenses generally, and that he had no experience in the determination of a reasonable royalty after infringement under § 284. Scofield specifically assumed, for purposes of his testimony, that there existed in the present ease acceptable non-infringing substitutes. He further ignored evidentiary facts considered relevant by this and other circuits. The analysis of this court in Egry, 23 F.2d at 443, is instructive:

In fixing a reasonable royalty, the primary inquiry, often complicated by secondary ones, is what the parties would have agreed upon, if both were reasonably trying to reach an agreement. This must be modified by the commercial situation, and when the result is to interfere with a patent monopoly, which the patentee was in position to and desired to keep, by retaining the entire market himself, his compensation for parting against his will with that opportunity must take due account of the loss to him of anticipated profits on the business which the licensees will thus get away from him. It is a step further, and we think a necessary one, to say that, when the patentee’s business scheme involves a reasonable expectation of making future profits by the continuing sale to the purchaser of the patented machine, of supplies to be furnished by the patentee, which future business he will lose by licensing a competitor to make the machine, this expectant loss is an element to be considered in retroactively determining a reasonable royalty; and this is so even though the expectation of such future business was not the result of any system of contract obligations, but was only expectation reasonably based on established business methods and customs.

In Georgia-Pacific, supra, the appellate court affirmed the analysis made by the district court at 318 F.Supp. at 1127, 116 USPQ at 243-44:

The amount of profits that USP [patent owner] was making and could (in February 1955 [when the infringement commenced]) reasonably expect to continue to make on its sales of Weldtex by licensing no one to sell Weldtex in the United States is of major relevance to the determination of the amount of royalty that USP would accept from GP and that GP would offer. USP was enjoying the profits of a readily salable product. USP was in a position to retain the entire market on striated fir plywood for itself. The result of GP’s infringement was to interfere ■ with that monopoly and, as planned, to put GP in direct competition with USP’s Weldtex throughout the period of infringement. The hypothetical license would have been one whereby GP would have been permitted to market striated fir plywood through the United States (as GP infringingly did).

* * * *

In the hypothetical negotiations, USP would have been reasonable in taking the position that it would not accept a royalty significantly less than the profit it was making by its policy of licensing no one *1164to sell striated fir plywood in the United States.

Attorney Scofield may well have been “persuasive,” but his testimony was based on general experience and invalid assumptions. There was clear error therefore in finding (4), that Scofield’s testimony was “in line with the factual realities of this case.”

Finding (5) was erroneously based on Stahlin’s actual overall profit in all its products and on absence of proof of Stahlin’s actual profit on its infringing sales. The infringer’s profit element, in the post-judgment “reasonable royalty” equation, is not related to the infringer’s actual profit; nor is it designed to insure the anomalous result of guaranteeing an actual profit to an infringer (or the profit it would have made if there had been no infringement). The licensee-profit element is but one of the measures applicable in March 1962, and should be based on the customary profit allowed licensees in the industry at that time. Whether, as events unfurled thereafter, Stahlin would have made an actual profit, while paying the royalty determined as of March 1962, is irrelevant. If there had been no infringement, and if Stahlin had actually agreed to pay a royalty in March 1962, and if that royalty rate had then proven onerous, Stahlin might have renegotiated the royalty rate or canceled the license. But those options are no longer available to Stahlin, and their consideration in a formula for setting the royalty rate which would have been reasonable in March 1962 was error.

Conclusion

Elements necessary to the determination of a reasonable royalty in the present case — Panduit’s actual profit margin in March 1962, and the customary profit allowed licensees in the electrical duct industry,11 — were not determined by the master in his report and cannot be discerned from the record.12 They therefore must be determined on remand. On remand, the following factors must also be considered: (1) the lack of acceptable noninfringing substitutes, (2) Panduit’s unvarying policy of not licensing the Walch patent, (3) the future business and attendant profit Pan-duit would expect to lose by licensing a competitor, and (4) that the infringed patent gave the entire marketable value to the infringed duct.13

For the reasons stated, we reverse the district court’s determination of a reasonable royalty, and remand the case for further proceedings consistent herewith.

MOORE, Circuit Judge.

Frank Gaylord appeals from the judgment of the Court of Federal Claims awarding him $5,000 for the United States Postal Service’s copyright infringement of his statutes. Because the trial court incorrectly limited Mr. Gaylord’s damages to the Postal Service’s highest past license payment and denied prejudgment interest, we vacate and remand for a determination of the market value of the Postal Service’s infringing use and an award of prejudgment interest.

*1341Background

Mr. Gaylord is the creator of “The Column,” a group of nineteen stainless steel sculptures representing a platoon of soldiers. The Column is the centerpiece of the Korean War Veterans’ Memorial on the National Mall in Washington, D.C. In 2002, the United States Postal Service issued a 37-cent stamp commemorating the 50th anniversary of the armistice of the Korean War. The stamp featured a photograph of The Column, which the Postal Service licensed from photographer John Alii. The Postal Service issued roughly 86.8 million of the stamps, sold retail goods carrying the stamp image, and licensed the stamp image to retailers. The Postal Service did not seek or obtain Mr. Gaylord’s permission to depict The Column on the stamp or the related merchandise.

In 2006, Mr. Gaylord sued the United States under 28 U.S.C. § 1498(b) for copyright infringement. In Gaylord v. United States, we held that Mr. Gaylord owned the copyright to The Column and that the Postal Service was liable for infringement. 595 F.3d 1364, 1381 (Fed.Cir.2010). We identified three general classes of infringing items: (1) stamps that were used to send mail; (2) unused stamps retained by collectors; and (3) retail goods featuring an image of the stamp. Id. at 1371. We remanded for a determination of damages.1 Id.

On remand, the Court of Federal Claims rejected Mr. Gaylord’s claim for a 10% royalty on about $30.2 million in revenue allegedly generated by the Postal Service’s infringing use, as well as his claim for prejudgment interest. Gaylord v. United States, 98 Fed.Cl. 389, 390, 392-93 (2011). The court reasoned that neither 28 U.S.C. § 1498(b), which waives the United States’ sovereign immunity for copyright infringement, nor the copyright infringement statute, 17 U.S.C. § 504, authorizes a royalty-based award for copyright infringement. Id. at 392. Instead, the court concluded that the proper measure of damages is “the approach in Steve Altman Photography of employing a ‘zone of reasonableness’ to determine the copyright owner’s actual damages.” Id. at 391 (citing Steve Altman Photography v. United States, 18 Cl.Ct. 267, 279 (1989)).

Applying this framework, the Court of Federal Claims determined that the “zone of reasonableness” for the value of a license on Mr. Gaylord’s copyright was between $1,500 and $5,000. Id. at 391-92. To set the lower bound, the court relied on the fact that the Postal Service paid photographer John Alii $1,500 to license the photo he took of The Column. Id. To set the maximum amount of available damages, the court relied exclusively on testimony by Mr. McCaffrey, the Postal Service’s Manager of Stamp Development, that the Postal Service had never paid more than $5,000 to license an existing image for use on a stamp. Id. at 392. Based on these facts, the court awarded Mr. Gaylord a one-time royalty of $5,000, which it determined was “reasonable and just compensation” for the government’s infringement. Id. The court explained that it was awarding Mr. Gaylord the highest amount within the “zone of reasonableness” because he was deprived of the opportunity to negotiate. Id.

The court also held that, even if reasonable royalties were allowed, Mr. Gaylord’s request for a 10% royalty was unreasonable because $3 million is outside the zone of reasonableness. The court based this conclusion on the Postal Service’s assertion that it had a policy against paying a royalty for stamp designs. Id. The trial court *1342rejected Mr. Gaylord’s claim for prejudgment interest because it found no explicit waiver of sovereign immunity allowing such a recovery. Id. Mr. Gaylord appeals the court’s decision that he is not entitled to a reasonable royalty or prejudgment interest. We have jurisdiction under 28 U.S.C. § 1295(a)(3).

Discussion

“On appeal from the Court of Federal Claims, this court reviews legal conclusions de novo and fact findings for clear error.” Columbia Gas Sys., Inc. v. United States, 70 F.3d 1244, 1246 (Fed.Cir.1995). “We review a damages award by the Court of Federal Claims for an abuse of discretion.” Hi-Shear Tech. Corp. v. United States, 356 F.3d 1372, 1377 (Fed.Cir.2004).

I. Damages

Mr. Gaylord argues that the trial court erred as a matter of law by holding that royalty damages are not available in copyright cases. He argues that other circuits allow hypothetical licenses as a measure of actual damages, and because reasonable royalties are the presumptive award under 28 U.S.C. § 1498(a), they should also be the presumptive award under § 1498(b). Mr. Gaylord argues that the Postal Service’s internal policies should not foreclose his request for a royalty-based award. He also contends that using the Postal Service’s highest past payment as the maximum amount recoverable was erroneous because the court should have considered real-world evidence of a reasonable royalty. For example, at trial Mr. Gaylord introduced evidence of his past licenses of The Column for various collectibles, such as t-shirts and miniature statues. He argues that the 10% royalty he typically received under such agreements accurately represents the fair market value of a license to his work. Mr. Gaylord also argues that his stamp was more popular than others, and thus warrants a higher license fee than the trial court awarded.

The Postal Service argues that the court awarded Mr. Gaylord “the highest lost license fee supported by the evidence” and “correctly employed a willing buyer/willing seller analysis and awarded Mr. Gaylord a lost license fee in the form of a $5,000 onetime lump-sum royalty, the highest ‘amount he would have received as a onetime fee in negotiations with the Postal Service.’ ” Appellee’s Br. 12 (citing Gay-lord, 98 Fed.Cl. at 392). It argues that making royalty damages presumptive in copyright cases would make § 1498(b)’s allowance of minimum statutory damages superfluous. The Postal Service calls Mr. Gaylord’s request for $3 million based on a 10% license speculative, arguing that Mr. Gaylord relies upon licenses that are not comparable to the infringing use. It also argues that the Korean War stamp was actually the least retained commemorative stamp issued around the same time. The Postal Service argues that the $5,000 award is an accurate measure of “just compensation” because it represents “the market value of the property at the time of the taking.” Id. at 12,19.

Section 1498(b), which waives the United States’ sovereign immunity for copyright infringement, states:

whenever the copyright in any work protected under the copyright laws of the United States shall be infringed by the United States ... the exclusive action which may be brought for such infringement shall be an action by the copyright owner against the United States in the Court of Federal Claims for the recovery of his reasonable and entire compensation as damages for such infringement, including the minimum statutory damages as set forth in [17 U.S.C. § 504(c)]....

*134328 U.S.C. § 1498(b) (emphasis added). In Leesona Corp. v. United States, our predecessor court interpreted “reasonable and entire compensation” in the context of § 1498(a), which waives the United States’ sovereign immunity for patent infringement. 599 F.2d 958 (Ct.Cl.1979). The Leesona court found “no clear indication that the government intended to assume responsibility for any payment other than the just compensation required by the fifth amendment.” Id. at 968. The Leesona court thus limited “reasonable and entire compensation” under § 1498(a) to a reasonable royalty for “a compulsory compensable license in the patent” or, when that “cannot be ascertained, another method of estimating the value of the lost patent.” Id. Punitive damages that may be available in a suit under Title 35, such as enhanced damages and attorneys’ fees, were excluded because they grant more than “just compensation.” Id. at 968. The court explained that “the proper measure ... is what the owner has lost, not what the taker has gained.” Id. at 969.

This analysis applies with equal force in the § 1498(b) context, where courts must determine just compensation for the plaintiffs loss when the government takes what is essentially a compulsory, non-exclusive license on the plaintiffs copyright. “Reasonable and entire compensation” entitles copyright owners to compensatory damages, including the minimum statutory damages, but not to non-compensatory damages. We conclude that the methods used to determine “actual damages” under the copyright damages statute, 17 U.S.C. § 504, are appropriate for measuring the copyright owner’s loss. When, as in this case, the plaintiff cannot show “lost sales, lost opportunities to license, or diminution in the value of the copyright,” many circuits award actual damages based on “the fair market value of a license covering the defendant’s use.” See On Davis v. The Gap, Inc., 246 F.3d 152, 164, 172 (2d Cir.2001); see also Thoroughbred Software Int’l, Inc. v. Dice Corp., 488 F.3d 352, 359-60 (6th Cir.2007); Jarvis v. K2 Inc., 486 F.3d 526, 533-34 (9th Cir.2007); McRoberts Software, Inc. v. Media 100, Inc., 329 F.3d 557, 566 (7th Cir.2003). The value of this license should be calculated based on a hypothetical, arms-length negotiation between the parties. See, e.g., Jarvis, 486 F.3d at 533 (“[I]n situations where the infringer could have bargained with the copyright owner to purchase the right to use the work, actual damages are what a willing buyer would have been reasonably required to pay to a willing seller for plaintiffs’ work.”).

It is incorrect in a hypothetical negotiation inquiry for a court to limit its analysis to only one side of the negotiating table because the court’s task is to determine the “reasonable license fee on which a willing buyer and a willing seller would have agreed for the use taken by the infringer.” See On Davis, 246 F.3d at 167. The trial court erred in this case by restricting its focus to the Postal Service’s past payments: $l,500-$5,000. Defendants cannot insulate themselves from paying for the damages they caused by resting on their past agreements and by creating internal “policies” that shield them from paying fair market value for what they took. See Rite-Hite Corp. v. Kelley Co., 56 F.3d 1538, 1555 (Fed.Cir.1995) (“[W]hat an infringer would prefer to pay is not the test for damages.”). Instead, the trial court must look at the evidence presented by both sides to determine the fair market value of a license to which the parties would have agreed. Hence, while the evidence may indicate that the Postal Service has not paid more than $5,000, it is equally clear that Mr. Gaylord has consistently licensed images of The Column for retail and commemora*1344tive items at approximately 10%. See, e.g., J.A. 1180-81,1201,1721.

The trial court legally erred in this case by failing to calculate the fair market value of a license based on a hypothetical negotiation between Mr. Gaylord and the Postal Service. In applying the so-called “zone of reasonableness” test, the court improperly limited its inquiry to the Postal Service’s past licenses and, as a result, erroneously capped Mr. Gaylord’s maximum damages without considering other evidence supporting a higher award. Moreover, the court gave undue weight to the Postal Service’s self-serving testimony that it is prohibited from paying an ongoing royalty on stamps, and as a result failed to consider whether the fair market value of a license would include an ongoing royalty rather than a one-time fee. See Gaylord, 98 Fed.Cl. at 392. We thus vacate and remand for the court to determine the fair market value of a license for the full scope of the Postal Service’s infringing use based on a hypothetical negotiation with Mr. Gaylord.

On remand, the trial court must consider all evidence relevant to a hypothetical negotiation rather than limiting its analysis to the Postal Service’s past licenses for different works or to the Postal Service’s internal policies.2 For example, Mr. Gay-lord presented evidence that he typically agreed to a royalty rate of 8-10% in past agreements licensing his work for use on various collectibles, such as miniatures and t-shirts. In one such agreement, Mr. Gay-lord earned $16,666.66 up front and a 10% royalty on all sales. The record also shows that Mr. Alii entered a license agreement with the architects of the Korean War Veterans’ Memorial, who he incorrectly believed held the copyright on The Column. Mr. Alii agreed to pay a 10% royalty to the architects for his sales and licensing of his photograph of The Column, which totaled $31,766.50 up to the date of the agreement.3 Finally, the Postal Service itself licensed the stamp image to third parties for use on retail goods in exchange for a royalty of 8% of sales. The Postal Service earned $17,831.93 under those agreements. Such evidence of past license agreements for the work in question is certainly relevant to a hypothetical negotiation analysis.

The trial court’s analysis of a hypothetical negotiation between Mr. Gaylord and the Postal Service may lead it to conclude that different license fees are appropriate for the three categories of infringing goods we identified in our previous opinion: (1) stamps used to send mail; (2) unused stamps purchased by collectors; and (3) commercial merchandise featuring an image of the stamp. Gaylord, 595 F.3d at 1371. For stamps used as postage, the trial court must determine whether an ongoing royalty or a one-time fee more accurately captures the fair market value of a license. For example, the court may consider evidence regarding whether people used the stamp at issue specifically because it featured an image of The Column or whether the stamp’s value is primarily attributable to its ability to send mail rather than to the image it depicts. While it is certainly permissible for the court to conclude that a lump sum license might be *1345appropriate, the court should not arbitrarily cap this award at $5,000 simply because the Postal Service claims it has never paid more to license a copyright for use on a stamp.

The analysis likely will differ for the value attributable to the Postal Service’s use of Mr. Gaylord’s work on the estimated $5.4 million of sold but unused stamps, including those retained by collectors, which represent nearly pure profit for the Postal Service. It may be pertinent to examine whether the number of unused stamps is greater for this stamp than for the average stamp issued by the Postal Service. Collectors may retain stamps for any number of reasons, including a preference for the image itself or a desire to obtain a particular stamp to complete a collection. See, e.g., J.A. 1217, 1262-63. The court should thus consider whether the evidence supports an ongoing royalty for unused stamps, and at what rate. We, however, do not rule out the possibility that a one-time, paid-up license accurately reflects the fair market value of a license for both the used and unused stamps.

The commercial merchandise seems distinctly different from the stamps. The Postal Service itself licensed the stamp image to third parties to be used on various retail goods for an 8% royalty, and it earned $17,831.93 in royalty payments. This is completely consistent with the 8-10% royalty rate Mr. Gaylord typically earned for licensing his work to third parties to be used on retail goods. It is also similar to the 10% royalty Mr. Alii agreed to pay for selling prints of his photograph of The Column. Based on these facts, an ongoing royalty appears to be appropriate for retail goods depicting Mr. Gaylord’s work, particularly those on which the Postal Service earned an 8% ongoing royalty. The trial court should also consider whether the evidence similarly supports an ongoing royalty for the $330,000 in revenue the Postal Service made from direct sales of pins, postcards, magnets, framed art, cancellation keepsakes, and other philatelic collectibles depicting the stamp. The court should keep in mind that Mr. Gay-lord’s recovery is not limited to the Postal Service’s actual profits. See Golight, Inc. v. Wal-Mart Stores, Inc., 355 F.3d 1327, 1338 (Fed.Cir.2004). Indeed, the court may find that a hypothetical negotiation between the parties would result in a higher ongoing royalty than the rate earned by Mr. Gaylord or the Postal Service under past agreements.

II. Prejudgment Interest

Mr. Gaylord argues that he is entitled to prejudgment interest. He cites Waite v. United States, in which the Supreme Court held that sovereign immunity does not prevent the award of prejudgment interest under the precursor to § 1498 because “reasonable and entire compensation” includes delay compensation. 282 U.S. 508, 508-09, 51 S.Ct. 227, 75 L.Ed. 494 (1931). The Postal Service concedes that the trial court failed to consider Waite, and thus that it erred 'by holding that sovereign immunity bars the award of prejudgment interest under § 1498. The Postal Service argues, however, that prejudgment interest should be denied in this case because Mr. Gaylord “cited no law or facts” in support of his request at trial. The Postal Service’s waiver argument is incorrect. Mr. Gaylord twice explicitly cited Waite to the trial court when arguing his entitlement to prejudgment interest. Mr. Gaylord is entitled to prejudgment interest because it is necessary to make his compensation complete. We vacate the trial court’s decision denying prejudgment interest and remand.

VACATED AND REMANDED.

*1346Costs

Costs to Plaintiff-Appellant.

Copyright Infringement; Measure of Damages for Postal Service’s Use of Copyrighted Image on Postage Stamp; 28 U.S.C. § 1498 (b); 17 U.S.C. § 504; Zone of Reasonableness Based Upon Evidentiary Record.

OPINION AND ORDER

WHEELER, Judge.

This case is before the Court on remand from the United States Court of Appeals for the Federal Circuit to determine the proper amount of damages due Plaintiff Frank Gay-lord. The Federal Circuit instructed this Court to determine the fair market value of a license for the Postal Service’s infringing use of Mr. Gaylord’s copyright. Gaylord v. United States, 678 F.3d 1339, 1340 (Fed.Cir.2012) (“Gaylord II”). The value of this license represents the amount Mr. Gaylord would have received if the Postal Service had paid Mr. Gaylord to use his copyright, instead of using it without his permission.

For the reasons explained below, the Court finds that Mr. Gaylord is entitled to just compensation of $684,844.94. The Court bases this conclusion on a finding that a 10 percent running royalty accurately captures the fair market value of a license to Mr. Gaylord’s copyright.

A detañed factual history of this case can be found in the Court’s previous opinions. See Gaylord v. United States, 85 Fed.Cl. 59 (2008); Gaylord v. United States, 98 Fed.Cl. 389, 390 (2011). The Court will provide a brief overview of the facts relevant to the issues currently on remand.

In 2006, Mr. Gaylord filed suit in this Court alleging that the Postal Service infringed upon his copyright in “The Column,” a group of nineteen stainless steel soldiers that forms the centerpiece of the Korean War Veterans Memorial on the National Mall. (Joint Stipulation (“Stip.”) ¶ 5, May 16, 2008.) The Court conducted a trial in Washington, D.C. from June 16 to June 20, 2008 and found that Mr. Gaylord owned a valid copyright for “The Column” but that the Postal Service made fair use of the “The Column” and therefore was not liable for copyright infringement. Gaylord, 85 Fed.Cl. at 68. On appeal, the Federal Circuit determined that the Postal Service’s depiction of the sculptures on its memorial stamp did not. fall within fair use and found that the Postal Service had infringed Mr. Gaylord’s copyright in three categories: (1) stamps used to send mail; (2) unused stamps retained by collectors; and (3) retail goods featuring an image of the stamp. Gaylord v. United States, 595 F.3d 1364, 1371 (Fed.Cir.2010) (“Gaylord I ”). The Federal Circuit remanded the case for a determination of damages. Id.

*541On April 22, 2011, this Court awarded $5,000 in damages to Mr. Gaylord representing the largest amount the Postal Service had ever paid to use an image on a stamp. Gaylord, 98 Fed.Cl. at 393. Mr. Gaylord appealed the damages award, and the Federal Circuit vacated this Court’s order and remanded the case for a determination of the fair market value of the Postal Service’s infringing use. Gaylord II, 678 F.3d at 1340. This Court conducted a remand trial on damages in Washington, D.C. during May 13-14, 2013. Thereafter, the parties submitted post-trial briefs on July 19, 2013 and reply briefs on August 1, 2013. The Court heard closing arguments on August 20, 2013.

Findings of Fact

In January 1996, amateur photographer John Alii visited the Korean War Veterans Memorial (“KWVM”) during a snowstorm and took a photograph that he called “Real Life.” (Stip. ¶ 12.) In 2002, the Postal Service authorized the 37-cent KWVM stamp that incorporated “Real Life” into the stamp image. (Stip. ¶ 13.) Mr. Gaylord did not consent to the Postal Service’s use of an image of “The Column” on the stamp. (Stip. ¶ 16.) The Postal Service released the KWVM stamp on July 27, 2003. (Stip. ¶ 14.) Between the time of the stamp’s release and March 31, 2005, when it was retired, the Postal Service sold 47,910,587 KWVM stamps. (Stip. ¶ 18.) Many of these stamps were used to send mail, but others were retained by collectors.

Between 1999 and 2012, the Postal Service conducted a quarterly survey through the marketing research firm Synovate (“Syno-vate survey”) to determine how many stamps would be retained by collectors. For the quarter that the KWVM stamp was issued, the Postal Service expected that at least 14,500,000 KWVM stamps would be retained by collectors. Collected stamps represent almost pure profit to the Postal Service because collected stamps are not exchanged for postal services, and the costs associated with printing and distributing stamps are minimal. (Trial II, Faris, Tr. 109.) As such, the 14,-500,000 collected stamps represented $5,400,000 that the Postal Service expected to retain in profit. (PX 29.) In addition to the used and collected stamps, the Postal Service also sold merchandise carrying the stamp image. (Stip. ¶ 15.) The Postal Service received $330,919.49 in revenue from the sales of retail goods that featured the KWVM stamp. (Stip. ¶ 22.)

Discussion

Cases before this Court on remand are governed by the mandate rule. Carolina Power & Light Co. v. United States, 98 Fed.Cl. 785, 794 (2011). “[E]very appellate court judgment vests jurisdiction in the trial court to carry out some further proceedings.” Exxon Chem. Patents, Inc. v. Lubrizol Corp., 137 F.3d 1475, 1483 (Fed.Cir.1998). The district court’s actions on remand “should not be inconsistent with either the letter or the spirit of the mandate.” Laitram Carp. v. NEC Carp., 115 F.3d 947, 950-51 (Fed.Cir.1997). Mandates should be interpreted by looking at the language of the judgment in combination with the accompanying opinion. Exxon Chem., 137 F.3d at 1483 (citing, inter alia, In re Sanford Fork & Tool Co., 160 U.S. 247, 256, 16 S.Ct. 291, 40 L.Ed. 414 (1895)).

Here, the Federal Circuit remanded the case for a determination of the “fair market value of a license for the full scope of the Postal Service’s infringing use.” Gaylord II, 678 F.3d at 1344. The Federal Circuit’s mandate requires the Court to calculate the value of this license based on “a hypothetical, arms-length negotiation between the parties.” Id. at 1343 (citing Jarvis v. K2 Inc., 486 F.3d 526, 533-34 (9th Cir.2007)).

Furthermore, the Federal Circuit suggested that this Court consider whether different license fees were appropriate for the three categories of infringing goods identified in the Federal Circuit’s 2010 opinion: (1) stamps used to send mail; (2) unused stamps purchased by collectors; and (3) commercial merchandise featuring an image of the stamp. Gaylord I, 595 F.3d at 1371.

Determining the fair market value of a license to “The Column” based on the legal fiction of a hypothetical negotiation involves “more the talents of a conjurer than those of a judge.” Fromson v. Western Litho Plate & Supply Co., 853 F.2d 1568, 1574 (Fed.Cir. *5421988). The Government’s infringement deprived Mr. Gaylord of the opportunity to negotiate with the Postal Service for compensation, and so this Court must surmise what would have occurred if Mr. Gaylord and the Postal Service had both come to the negotiation table on July 27, 2003 to decide on a price for a license to use “The Column.” After a full review of the evidence presented by both sides, the Court’s undertaking of this task follows.1

I. Stamps Used to Send Mail

The Federal Circuit’s mandate instructs this Court to determine whether an ongoing royalty or a one-time fee more accurately captures the fair market value of a license for stamps used to send mail. As the Federal Circuit noted, it is difficult to know whether stamps in this category were purchased by consumers because the KWVM stamp featured an image of “The Column” or simply because the stamp was needed to send mail. Due to the difficulty of calculating damages, counsel for Mr. Gaylord does not seek damages for stamps used to send mail, and the Court awards Mr. Gaylord no damages for this category.

II. Unused Stamps Purchased by Collectors

As the Federal Circuit explained, the analysis for unused stamps purchased by collectors differs from used stamps because unused stamps “represent nearly pure profit for the Postal Service.” Gaylord, 678 F.3d at 1345. The Federal Circuit instructed the Court to consider whether the evidence supports an ongoing royalty rate or a lump sum royalty payment for the estimated $5.4 million collected by the Postal Service from unused stamps. The Court finds that a 10 percent running royalty is the appropriate approach for assessment of damages.

Mr. Gaylord has consistently licensed images of “The Column” for retail and commemorative items at approximately a 10 percent running royalty. At trial, Mr. Gaylord introduced evidence of his past licenses of “The Column” for various collectibles, such as t-shirts and miniature statues, for which he received a 10 percent royalty. (PX 17, 18, 24,42; DX 40, 41.)

Furthermore, in the hypothetical negotiation between the Postal Service and Mi’. Gay-lord, the Postal Service had a strong financial incentive to enter into a license agreement with Mr. Gaylord. Stamps purchased by collectors represent nearly pure profit to the Postal Service and so the Postal Service stood to receive a significant profit from the KWVM stamp. The record shows that the Postal Service expected the KWVM stamp to sell well among collectors. Commemorative stamps are profitable for the Postal Service and military-themed stamps sell especially well. (Trial II, Delaney, Tr. 328-29.) Indeed, the Synovate surveys produced by the Postal Service show that the KWVM stamp was in the top 25 percent of its class of 37-cent commemorative stamps with respect to projected retention revenue. (DX 125, 131, 135,136.) The Postal Service believed at the time of the hypothetical negotiation that the KWVM stamp would sell more than the average commemorative stamp because it decided to print 86 million KWVM stamps, which exceeds the average print run for commemorative stamps of 50-60 million stamps. (Trial I, Delaney, Tr. 455-56.)

For these reasons, the Court finds that a 10 percent running royalty fairly represents the fair market value of a license to Mr. Gaylord’s work. Thus, after applying a 10 percent royalty to the estimated $5.4 million collected by the Postal Service, Mr. Gaylord is entitled to $540,000 in damages for stamps purchased by collectors.

III.Commercial Merchandise Featuring an Image of the Stamp

The Federal Circuit also instructed the Court to determine the damages for the *543$330,919.49 that the Postal Service received on merchandise sales featuring images of the KWVM stamp. The record reflects that Mr. Gaylord has consistently licensed images of “The Column” for retail and commemorative items at approximately a 10 percent royalty. In a hypothetical negotiation, Mr. Gaylord would likely have received a 10 percent royalty on merchandise. Applying the 10 percent royalty to the estimated $330,919.49 collected by the Postal Service, Mr. Gaylord is entitled to $33,092 in damages for merchandise featuring an image of the stamp.

IV. Percent Delay Compensation Factor

Lastly, the Federal Circuit determined that Mr. Gaylord is entitled to prejudgment interest because it is “necessary to make his compensation complete.” Gaylord II, 678 F.3d at 1345 (citing Waite v. United States, 282 U.S. 508, 508-09, 51 S.Ct. 227, 75 L.Ed. 494 (1931)). The Government and Mr. Gay-lord have stipulated to a delay compensation interest percentage factor of 19.5 percent to be added to any damages assessed by the Court. (Stipulation, Aug. 26, 2013.) This Court finds that Mr. Gaylord is entitled to $573,092 in damages for merchandise and unused stamps. Applying the 19.5 percent factor to $573,092 results in a prejudgment interest factor of $111,752.94. In total, the Court awards Mr. Gaylord $684,844.94.

Conclusion

Based upon the foregoing, the Court awards damages to Plaintiff of $684,844.94. The Court directs the Clerk to enter judgment in favor of Plaintiff in that amount. No costs.

IT IS SO ORDERED.

PER CURIAM:

Appellant Cream sued appellees alleging that music in a TV commercial prepared by Benton and Bowles to advertise Schlitz beer infringed appellant’s copyright on a popular rhythm and blues composition, “The Theme from Shaft.”

The jury found infringement. By agreement of the parties the issue of damages was submitted to the court which awarded Cream a total of $17,000. Cream appealed.

DAMAGES

Schlitz applied to Cream for a one-year license to use the Shaft theme music in its commercial. Cream quoted a fee of $100,000. (Cream conceded at trial, and the district court found, that the market value of such a license was $80,000.) After Schlitz failed to take a license, another manufacturer approached Cream for a license but withdrew when the Schlitz commercial was aired. There was testimony that use of a well-known popular song in a commercial destroys its value to other advertisers for that purpose.

The district court awarded Cream $12,-000 in damages for loss of the license fee. The court reasoned that the value of a license for use of the entire song for a year was $80,000, that only a small portion of the song was actually used in the Schlitz commercial, and the reasonable value of a license for use of that portion was 15% of the value of a license to use the entire song.

The only evidence before the court was that unauthorized use of the Shaft theme music in Schlitz’s commercial ended Cream’s opportunity to license the music for this purpose. There was no evidence that Schlitz sought, or Cream was willing to grant, a license for use of less than the entire copyrighted work, that a license limited to the portion used in the commercial would have had less value, or that use limited to this portion would have had a less devastating effect upon Cream’s opportunity to license to another. Since de*828fendants’ unauthorized use destroyed the value of the copyrighted work for this purpose, plaintiff was entitled to recover that value as damages. 3 Nimmer, The Law of Copyright, § 14.02 at 14-6 (1984).

PROFITS

17 U.S.C. § 504(b) (1982) provides that, in addition to actual damages suffered as a result of the infringement, the copyright owner is entitled to recover “any profits of the infringer that are attributable to the infringement and are not taken into account in computing the actual damages.” The statute also defines and allocates the burden of proof, providing, “[i]n establishing the infringer’s profits, the copyright owner is required to present proof only of the infringer’s gross revenue, and the infringer is required to prove his or her deductible expenses and the elements of profit attributable to factors other than the copyrighted work.”

Schlitz. Cream offered proof that Schlitz’s profit on malt liquor for the period during which the infringing commercial was broadcast was $4.876 million. Cream sought to recover $66,800 as the portion of Schlitz’s profit attributable to the infringement, arguing that the expenditure for the infringing commercial constituted 13.7% of Schlitz’s advertising budget for the year, the infringing music was responsible for 10% of the commercial’s advertising power, and, therefore, 1.37% of the profit on malt liquor were attributable to the infringement.

The district court concluded that the infringement “was minimal,” consisting principally of a ten-note ostinato, and that the infringing material did not add substantially to the value of the commercial. The court also concluded, however, that the commercial was successful, that “it sold some beer,” and “that the music had a portion of that.” The court continued, “So I have to find some profit of the defendants which is allocable to the infringement, but, as I say, I think it’s miniscule. I have interpolated as best I can. They made a profit of $5 million. One-tenth of 1 percent is $5,000, so I will add that____”

Cream argues that since it established Schlitz’s total profits from the sale of malt liquor, the burden was placed on Schlitz to prove any portion of the profits not attributable to the infringement, and since the defendants put on no evidence, Cream was entitled to recover the part of Schlitz’s profits it sought. The court’s lesser award, Cream argues, was wholly arbitrary, and supported by no evidence in the record.

Defendants respond that Cream failed to establish that any part of the profits from the sale of malt liquor were attributable to the commercial, much less to its infringing portion, and was therefore entitled to no share of the profits at, all. One of the court’s formal findings, prepared by defendants, might be read as stating that no causal connection had been shown between the infringement and defendants’ profits. It is clear from the court’s statements, including those quoted above, however, that the court concluded from the jury’s verdict and from the evidence that some of the profits from malt liquor sales were in fact attributable to the use of plaintiff’s copyrighted music in the commercial. The court determined the share of the profits attributable to the infringing material as best it could and awarded Cream Vioth of 1% of those profits. Defendants have not cross-appealed the judgment, and may not challenge the determination of causation upon which it rests.

We also reject Cream’s contention. Although the statute imposes upon the infringer the burden of showing “the elements of profit attributable to factors other than the copyrighted work,” 17 U.S.C. § 504(b), nonetheless where it is clear, as it is in this case, that not all of the profits are attributable to the infringing material, the copyright owner is not entitled to recover all of those profits merely because the infringer fails to establish with certainty the portion attributable to the non-infringing elements. “In cases such as this where an infringer’s profits are not entirely due to *829the infringement, and the evidence suggests some division which may rationally be used as a springboard it is the duty of the court to make some apportionment.” Orgel v. Clark Boardman Co., 301 F.2d 119, 121 (2d Cir.1962). As Learned Hand said in Sheldon v. Metro-Goldwyn Pictures Corp., 106 F.2d 45, 51 (2d Cir.1939), aff'd, 309 U.S. 390, 60 S.Ct. 681, 84 L.Ed. 825 (1940):

But we are resolved to avoid the one certainly unjust course of giving the plaintiffs everything, because the defendants cannot with certainty compute their own share. In cases where plaintiffs fail to prove their damages exactly, we often make the best estimate we can, even though it is really no more than a guess (Pieczonka v. Pullman Co., 2 Cir., 102 F.2d 432, 434), and under the guise of resolving all doubts against the defendants we will not deny the one fact that stands undoubted.

By claiming only 1.37% of Schlitz’s malt liquor profits, Cream recognizes the impropriety of awarding Cream all of Schlitz’s profits on a record that reflects beyond argument that most of these profits were attributable to elements other than the infringement. As to the amount of profits attributable to the infringing material, “what is required is ... only a reasonable approximation,” Sheldon v. Metro-Goldwyn Pictures Corp., 309 U.S. at 408, 60 S.Ct. at 688; see also Twentieth Century-Fox Film Corp. v. Stonesifer, 140 F.2d 579, 583-84 (9th Cir.1944); MCA, Inc. v. Wilson, 677 F.2d 180,186 (2d Cir.1981), and Cream’s calculation is in the end no less speculative than that of the court. The disparity between the amount sought by Cream and the amount awarded by the court appears to rest not so much upon a difference in methods of calculation as upon a disagreement as to the extent to which the commercial infringed upon the copyright and the importance of the copyrighted material to the effectiveness of the commercial. These were determinations for the district court to make.

The parties agreed that the issue of damages and profits would be tried to the court. The jury’s verdict did not expressly determine the degree to which the commercial infringed upon Cream’s copyright. The court’s factual findings, though perhaps unfavorable to Cream, do not conflict with the general verdict. Cf. Blake v. Hall, 668 F.2d 52, 54 (1st Cir.1981).

Benton. Cream claimed all of Benton’s profit from the TV commercial; the district court awarded none at all. In announcing its judgment the court initially overlooked the claim against Benton. When alerted to the omission the court said, “I will somehow incorporate that into the profit that I awarded with respect to the company. I can’t conceive of an award of more than the amount I gave. You can find Benton and Bowles’ profit in there by reducing the amount of profit of the beer company.”

Obviously it would be improper to assume the profits of the advertising company would be subsumed in the profits of the firm hiring it, if that was the court’s intention. Indeed, the profits of the advertising firm were necessarily excluded from the award against the hiring company, since, under § 504(b), Schlitz must be allowed to deduct the monies paid to the advertising firm in calculating its profits.

To avoid unjust enrichment of Benton as a result of its unlawful use of Cream’s copyrighted music, the district court must assess a separate award of damages against Benton by making a reasonable approximation of the portion of Benton’s profits due to the use of the infringing music.

Plaintiff is awarded costs on appeal including reasonable attorney’s fees in an amount to be determined by the district court.

Reversed and remanded for proceedings not inconsistent with this opinion.

OPINION

ROTH, Circuit Judge.

This appeal requires us to decide whether a showing of willful infringement is a prerequisite to an accounting of a trademark infringer’s profits for a violation of section 43(a) of the Lanham Act. We hold that wilfulness is an important equitable factor but not a prerequisite to such an award, noting that our contrary position in SecuraComm Consulting Inc. v. Securacom Inc., 166 F.3d 182, 190 (3d Cir.1999), has been superseded by a 1999 amendment to the Lanham Act. We further affirm the District Court’s resolution of several other damages issues, with a single exception explained below.

I. Factual Background and Procedural History

Joseph Renosky was a member of the board of directors of Banjo Buddies, Inc., (“Banjo Buddies” or “BBI”) from February 1996 until May 1999. Banjo Buddies’ principal product during that time was an extremely successful fishing lure called the Banjo Minnow, which Renosky helped develop.

The Banjo Minnow was principally advertised via “infomercial” broadcast, and was also sold in sporting goods catalogs and sporting goods stores. Tristar Products, Inc., obtained exclusive rights to advertise and sell the Banjo Minnow through all forms of “direct response marketing, ... print media, and retail distribution.” BBI received 48% of Tristar’s net profits in return. Renosky agreed to provide the manufactured Banjo Minnow lure kit through his corporation, Renosky Lures, Inc., to both Tristar and BBI at $5.20 per kit.1 Renosky received additional shares of BBI stock in exchange for producing the Banjo Minnow kits at a “fair price.” Re-nosky also executed a non-compete agreement in favor of BBI in exchange for more BBI stock. The Banjo Minnow sold very well for a little over a year, from mid-1996 through mid-1997, but then sales dwindled considerably. BBI introduced several derivative Banjo Minnow products in 1998, but none approached the success of the original.

During the Banjo Minnow’s early success in 1996, Renosky presented an idea to the BBI board for a “new and improved” Banjo Minnow called the Bionic Minnow.2 The board took no formal action on the proposal, and a month later Renosky advised one of BBI’s directors that he would develop the new lure independently. At least two board members urged Renosky against this course of action, but Renosky could not be swayed. He immediately began developing the Bionic Minnow through Renosky Lures and ultimately marketed *172the new lure via infomercial and other means beginning in February 1999.

After Renosky failed to comply with a “cease and desist” letter, BBI brought suit in the United States District Court for the Western District of Pennsylvania in April 1999. BBI alleged that Renosky violated section 43(a) of the Lanham Act, 15 U.S.C. § 1125(a), by developing and marketing the Bionic Minnow in such a way that customers would believe the Bionic Minnow was a Banjo Buddies product. BBI also alleged that Renosky’s conduct breached the non-compete contract and Renosky’s fiduciary duties as an officer of Banjo Buddies.3

The District Court denied cross-motions for partial summary judgment and held a five-day bench trial in May 2002. In its Findings of Fact and Conclusions of Law issued in November 2002, the court found that Renosky was liable for “false designation of origin” under § 43(a) of the Lan-ham Act.4 The court further found that Renosky breached his fiduciary duty of loyalty to Banjo Buddies by pursuing a corporate opportunity — the Bionic Minnow project — without fully disclosing his actions to the board or forcing the board to accept or reject the project. The court also found that Renosky breached the non-compete agreement by independently developing the Bionic Minnow. Finally, the court found that Renosky breached his fiduciary duty of good faith and fair dealing by overcharging BBI for the Banjo Minnow kits.

The District Court concluded that Reno-sky should be forced to disgorge the net profits of the Bionic Minnow project under section 35(a) of the Lanham Act, 15 U.S.C. § 1117(a), which provides for such ac-countings as an equitable remedy for Lan-ham Act violations. The District Court also concluded that the damages arising from Renosky’s usurpation of a corporate opportunity, breach of the non-compete contract, and overcharging for the Banjo Minnow lure kits were too speculative to support any monetary award.

Accordingly, the District Court ordered Renosky to pay to Banjo Buddies the net profits earned by the Bionic Minnow project, and to produce “verified financial records” attesting to this amount. Renosky never produced these records, despite numerous delays and court orders. Renosky did ultimately retain an independent financial analysis (the “Alpern Report”), which the District Court accepted for purposes of establishing the total sales of the Bionic Minnow through November 2002. However, the court rejected that report’s conclusion that the Bionic Minnow project suffered a net loss. Accordingly, the court calculated Renosky’s profits by multiplying the total sales figure by 16%, based on testimony from Renosky’s business manager that Renosky Lures products typically earn a “bottom line” of between 15-17%. The court also determined that Renosky *173should be forced to disgorge all of the distributions (based on gross sales) made to him as a shareholder in the Bionic Minnow project. The court entered judgment in March 2003 against Renosky in the amount of $1,589,155.

Banjo Buddies moved to alter or amend the District Court’s judgment pursuant to Federal Rule of Civil Procedure 59(e), arguing that the court erred by holding that the damages arising from Renosky’s overcharges for the Banjo Minnow lure kits were too speculative to support a monetary award. The District Court denied this motion in March 2003.

Renosky and BBI both appeal the District Court’s judgment. Renosky asserts that the District Court should not have ordered an accounting of profits because Renosky did not intentionally or willfully confuse or deceive customers. Renosky alternatively argues that the District Court’s calculation of those profits was clearly erroneous. Banjo Buddies cross-appeals, contending that the District Court erred by refusing to award damages for Renosky’s overcharges rather than make a reasonable estimate of damages based on the available evidence.

II. Jurisdiction and Standards of Review

The District Court had federal question jurisdiction over Banjo Buddies’ Lanham Act claim, 28 U.S.C. § 1331, supplemental jurisdiction over the parties’ state law claims, 28 U.S.C. § 1367, and diversity jurisdiction over all claims owing to the complete diversity of the parties, 28 U.S.C. § 1332. We have appellate jurisdiction to review the District Court’s final judgment. 28 U.S.C. § 1291.

We review the District Court’s factual findings under a clearly erroneous standard, but exercise plenary review over the District Court’s interpretation of legal questions and its application of the law to the facts. Castrol Inc. v. Pennzoil Co., 987 F.2d 939, 950 (3d Cir.1993). We further review the District Court’s award of equitable remedies under section 35(a) of the Lanham Act under an abuse of discretion standard. Gucci America, Inc. v. Daffy’s, Inc., 354 F.3d 228, 242 (3rd Cir.2003).

III. Discussion

A. Willfulness Is a Factor, Not a Prerequisite.

Renosky argues that the District Court erred by awarding profits from the Bionic Minnow project to Banjo Buddies under section 35(a) of the Lanham Act because Renosky’s violation of section 43(a) of that statute was not willful or intentional. Re-nosky relies on SecuraComm Consulting, Inc. v. Securacom, Inc., 166 F.3d 182 (3d Cir.1999), in which this court held that “a plaintiff must prove that an infringer acted willfully before the infringer’s profits are recoverable” under § 35(a) of the Lanham Act. Id. at 190 (citing George Basch Co. v. Blue Coral, Inc., 968 F.2d 1532, 1537 (2d Cir.1992)). The District Court’s findings related to the issue of Renosky’s intent are ambiguous and possibly contradictory.5 However, we need not decide whether the *174District Court found or should have found that Renosky acted willfully, because we conclude that SecuraComm’s bright-line willfulness requirement has been superseded by statute and that, based on all the relevant equitable factors, the District Court did not abpse its discretion by ordering an accounting of Renosky’s profits.

SecuraComm’s bright-line rule was the dominant view when SecuraComm was issued in January 1999. See, e.g., Quick Technologies, Inc. v. Sage Group PLC, 313 F.3d 338, 347-48 (5th Cir.2002) (collecting cases, including SecuraComm); George Basch Co., 968 F.2d at 1537; Restatement (Third) of Unfair Competition § 37 (1995); J. Thomas McCarthy, 5 McCarthy on Trademarks and Unfair Competition § 30:62 (4th ed.1996). In August 1999, however, Congress amended § 35. Prior to the amendment, that section provided as follows:

When a violation of any right of the registrant of a mark registered in the Patent and Trademark Office, or a violation under ' section 43(a) [15 U.S.C. § 1125(a)], shall have been established ... the plaintiff shall be entitled ..., subject to' the principles of equity, to recover' (1) defendant’s profits, (2) any damages sustained by the plaintiff, and (3) the costs of the action.

See SecuraComm, 166 F.3d at 186 (quoting former 15 U.S.C. § 1117(a)). The 1999 amendment replaced “or a violation under section 43(a)” with'“a violation under section 43(a), or a willful violation under section 43(c),” see Pub.L. No. 106413, § 3(b), 113 Stat. 219 (Aug. 5, 1999) (emphasis added). The plain language of the amendment indicates that Congress intended to condition monetary awards for § 43(c) violations, but not § 43(a) violations, on a showing of willfulness.6

We presume Congress was aware that most courts had consistently required a showing of willfulness prior to disgorgement of an infringer’s profits in Lanham Act cases, despite the absence of the word “willful” in the statutory text prior to 1999. See Scheidemann v. INS, 83 F.3d 1517, 1525 (3d Cir.1996) (“[W]e must presume that Congress is aware of existing judicial interpretations of statutes.”). By adding this word to the statute in 1999, but limiting it to § 43(c) violations, Congress effectively superseded the willfulness requirement as applied to § 43(a). See Russello v. U.S., 464 U.S. 16, 23, 104 S.Ct. 296, 78 L.Ed.2d 17 (1983) (“ ‘Where Congress includes particular language in one section of a statute but omits it in another section of the same Act, it is generally presumed that Congress acts intentionally and purposely in the disparate inclusion or exclusion.’ ”) (quoting United States v. Wong Kim Bo, 472 F.2d 720, 722 (5th Cir.1972)).

This conclusion is supported by Quick Technologies, 313 F.3d at 349, the only other appellate decision to reach the issue. The Fifth Circuit in Quick Technologies considered the effect of the 1999 amendment and held that, based on earlier decisions of that court as well as “the plain *175language of [§ 43(a) ],” willful infringement was not a prerequisite to an accounting of the infringer’s profits. Id. The court noted the wealth of contrary authority, including SecuraComm, but pointed out that all of those cases preceded the statutory change. Id. at 347-48. The Quick Technologies court reaffirmed the factor-based approach elaborated in prior Fifth Circuit cases, including Pebble Beach Co. v. Tour 18 I Limited, 155 F.3d 526, 554 (5th Cir.1998), explaining that the infringer’s intent was an important — but not indispensable — -factor in evaluating whether equity supports disgorging the infringer’s profits. Quick Techs., 313 F.3d at 349. These factors “include, but are not limited to (1) whether the defendant had the intent to confuse or deceive, (2) whether sales have been diverted, (3) the adequacy of other remedies, (4) any unreasonable delay by the plaintiff in asserting his rights, (5) the public interest in making the misconduct unprofitable, and (6) whether it is a case of palming off.” Id. (internal citations omitted).

In Gucci America, Inc. v. Daffy’s, Inc., 354 F.3d 228 (3d Cir.2003), the panel majority noted that the 1999 amendment might affect the continued validity of SecuraComm’s bright-line willfulness requirement. Id. at 239-40 (noting that statutory language and legislative history of the 1999 amendment “suggests that willfulness is a prerequisite in a trademark dilution cause of action, not an infringement action”). The majority determined it did not need to decide the issue, however, reasoning that even under the Quick Technologies factor-based approach, the District Court did not abuse its discretion in refusing to order an accounting of the infringer’s profits. Id. at 241-43 (“Accordingly, even after the 1999 amendments to the Lanham Act and any impact it may have had on our holding in SecuraComm, we nevertheless conclude that the district court did not abuse its discretion given the equities here, including Daffy’s good faith.”).7

For the reasons explained above, we now hold that SecuraComm has been superceded by the 1999 amendment. Relying on the Quick Technologies factor-based approach endorsed in Gucci America, we further conclude that the District Court did not abuse its discretion by ordering an accounting of Renosky’s profits. Apart from his contention that his violation was not willful, Renosky does not argue that the District Court abused its discretion. Accordingly, our consideration of the equities here will be brief. Because the District Court’s findings concerning Reno-sky’s intent are difficult to reconcile, see supra note 5, we will assume that factor is neutral. Nonetheless, all of the other Quick Technologies factors support an award of profits here.

It is likely that Renosky’s conduct diverted sales from Banjo Buddies. See Quick Techs., 313 F.3d at 349 (factor two). The District Court found that Renosky’s marketing for the Bionic Minnow was confusingly similar to that of the Banjo Minnow, noting numerous material similarities in the infomercials used to market each product. The court also found that the two lure kits were “nearly identical” and were packaged identically. The court further found that the markets for the two products were “either the same or substantially overlapping].” The District *176Court’s observations concerning the close similarities of the products as well as their packaging and marketing schemes also strongly support the conclusion that Reno-sky was “palming off’ the Bionic Minnow as a Banjo Buddies product. See id. (factor six). The public has an interest in discouraging this type of behavior, as it interferes with the consumer’s ability to make informed purchasing decisions. See id. (factor five).

Next, there are no other adequate remedies. See id. (factor three). The District Court rejected Banjo Buddies’ estimation of its damages (for both the Lanham Act claims and the state law claims) as too speculative. If Renosky’s profits are not assessed, Banjo Buddies will be wholly uncompensated for Renosky’s infringing actions. Finally, Banjo Buddies did not delay in bringing suit to stop Renosky’s infringing actions. See id. (factor four). Accordingly, we conclude that the District Court did not abuse its discretion in deciding to order an accounting of Renosky’s profits.

B. The District Court’s Estimation of Profits.

The remaining issues in Renosky’s appeal concern the District Court’s calculation of the amount of profits to be awarded. We first hold that the District Court did not clearly err by rejecting Renosky’s contention that he suffered a net loss on the Bionic Minnow project, and did not abuse its discretion by using an alternative method to estimate Renosky’s profits. See Tamko Roofing Products, Inc. v. Ideal Roofing Co., Ltd., 282 F.3d 23, 39 (1st Cir.2002) (calculation of profits under section 35(a) is left to the trial court’s discretion, and will not be disturbed unless “it rests on clearly erroneous findings of fact, incorrect legal standards, or a meaningful error in judgment”).

Section 35(a) provides that “[i]n assessing profits the plaintiff shall be required to prove defendant’s sales only; defendant must prove all elements of cost or deduction claimed.” 15 U.S.C. § 1117(a); see also Caesars World, Inc. v. Venus Lounge, Inc., 520 F.2d 269, 273 (3d Cir.1975). The District Court accepted the Alpern report’s figure for total sales of the Bionic Minnow through November 22, 2002. Thus, Banjo Buddies’ burden of proof was satisfied by Renosky’s accountant’s financial report.

However, the District Court held that Renosky failed to satisfy his burden of proof regarding costs and deductions. The District Court rejected the Alpern report’s conclusion that Renosky suffered a loss of $ 492,699.00 for several reasons, most of which Renosky makes no attempt to refute on appeal. First, the court observed that the Alpern report’s summary of direct expenses associated with the Bionic Minnow project — totaling almost five million dollars — was sorely lacking in detail, lumping costs into six broad categories with no explanation of what specific expenses those categories represented.8 Renosky appears to argue that the District Court improperly rejected the direct expense summary because the preparers of the Alpern report were unable to confirm expenses associated with Pacific Media, a vendor representing no more than two percent of the direct expenses associated with the Bionic Minnow. This argument is a red herring. The court rejected the summary in spite of the preparers’ success in obtaining corroboration from most ma*177jor vendors, not because of its failure to obtain corroboration from one.

Renosky fails to address the District Court’s remaining reasons for rejecting the Alpern report’s analysis of costs associated with the Bionic Minnow project. Most important, Renosky makes no attempt to explain why he twice failed to produce verified financial records supporting his claimed costs and deductions as ordered by the court.9 The court also observed several unexplained discrepancies between the Alpern report’s summary of direct expenses and other evidence in the record. Next, the court rejected the Alpern report’s conclusion that “shared expenses” associated with the Bionic Minnow project were $ 1,416,050. The court explained that the Alpern report did not show how “each item of general expense contributed to the production of the infringing items in issue and offer a fair and acceptable formula for allocating a given portion of overhead to the particular infringing items at issue.” (citing Design v. K-Mart Apparel Corp., 13 F.3d 559, 565-66 (2d Cir.1994)). Finally, the court found that the Alpern report’s “bottom line” lacked credibility. The court doubted that Renosky would allow the Bionic Minnow to lose nearly half a million dollars, and noted that Renosky’s claimed loss was inconsistent with his attempt to secure clarification that profits accrued after November 22, 2002, would belong to him and not Banjo Buddies. Considering the collective strength of these arguments together with Renosky’s failure to address most of them, we conclude that the District Court’s rejection of the Alpern report’s cost analysis was not clearly erroneous.

Because Renosky failed to meet his burden of proving costs and deductions, the District Court was forced to use an alternative method to estimate Renosky’s profits. The court decided to ’rely on the trial testimony of Renosky’s business manager, Denice Altemus, who stated that Re-nosky Lures products “always [make] a bottom line of between 15 and 17%.” Re-nosky argues that there is no direct evidence that the Bionic Minnow earned a profit in this range. While this is true, the onus of producing such evidence is clearly placed by § 35(a) on Renosky, not Banjo Buddies. 15 U.S.C. § 1117(a). The District Court has broad discretion in shaping remedies under § 35(a), see Burger King Corp. v. Weaver, 169 F.3d 1310, 1321 (11th Cir.1999), and did not abuse that discretion by estimating that the Bionic Minnow earned a profit of 16%.

Renosky further argues that Banjo Buddies is only entitled to 48% of whatever profits were earned by the Bionic Minnow project. That is, if Banjo Buddies had produced the Bionic Minnow, it would have received only 48% of the profits earned from the sale of the lure under its contract with TriStar. We first note that this contention is impossible to evaluate on appeal as a factual matter. Presumably Tri-Star provided some services in exchange for its profit-sharing agreement with Banjo Buddies, and presumably Renosky procured those same services through services contracts rather than a profit-sharing agreement. There is no way for this court to determine which party struck the better deal.

Further, this argument also fails as a matter of law, because there is no requirement that the defendant’s profits approximate the plaintiffs damages. Section 35(a) permits a plaintiff to recover, “subject to the principles of equity ..., (1) defendant’s profits, (2) any damages sustained by the plaintiff, and (3) the costs of *178the action.” 15 U.S.C. § 1117(a). As the Second Cirehit observed in George Basch, 968 F.2d at 1537, an accounting of the infringer’s profits is available if the defendant is unjustly enriched, if the plaintiff sustained damages, or if an accounting is necessary to deter infringement. These rationales are stated disjunctively; any one will do. See id. Allowing Renosky to keep half the estimated profits of his infringing activities would not serve the Congressional purpose of making infringement unprofitable — Renosky would be unjustly enriched and other would-be infringers would be insufficiently deterred. See Burger King Corp., 169 F.3d at 1321-22; Louis Vuitton S.A. v. Lee, 875 F.2d 584, 588-89 (7th Cir.1989); Playboy Enters., Inc. v. Baccarat Clothing Co., 692 F.2d 1272, 1274 (9th Cir.1982), Even if Banjo Buddies receives a windfall in this case— which, as discussed in the previous paragraph, is impossible for this court to determine — it is preferable that Banjo Buddies rather than Renosky receive the benefits of Renosky’s infringement. See Mishawaka Rubber & Woolen Mfg. Co. v. S.S. Kresge Co., 316 U.S. 203, 206-07, 62 S.Ct. 1022, 86 L.Ed. 1381 (1942).

Finally, we agree with Renosky that the District Court clearly erred by adding distributions made to Renosky as á shareholder in the Bionic Minnow project to the profits award because these distributions were already accounted for in the court’s estimation of profits. Financial records prepared by Renosky Lures’ business manager and introduced at trial by Banjo Buddies show that distributions were paid according to a simple formula: five percent of gross sales each month. Those records treat the distributions as an expense for bookkeeping purposes. That is, each month’s “Total Profit” was calculated by subtracting expenses from sales, and shareholder distributions (denominated “Return Reserve”) were considered expenses in this calculation. Banjo Buddies added the “Total Profit” and “Return Reserve” figures to arrive at a “Total Net Profit” figure which it then asked the District Court to assess as the measure of profits under section 35(a). This is sensible — distributing monies to shareholders is a method of disbursing income, not a business expense, and the distributions should be included in the District Court’s profits award. The District Court may have been attempting to apply this reasoning when it determined that Renosky’s share of the distributions should be added to the estimated profits award. However, when the District Court decided to estimate profits by multiplying the Alpern report’s gross sales figure by sixteen percent, rather than use the method proposed by Banjo Buddies, the issue created by Renosky Lure’s bookkeeping practice of treating distributions as expenses disappeared. The court’s estimate accounts for all of the profits of the Bionic Minnow project — the shareholder distributions, which amounted to five percent of gross sales, as well as an estimated eleven percent of additional profit.

C. Overcharge Damages.

Banjo Buddies argues on cross-appeal that the District Court erred by refusing to award monetary damages after determining that Renosky violated his fiduciary duty by overcharging Banjo Buddies for the Banjo Minnow lure kits. We hold that the District Court properly determined that Banjo Buddies failed to meet its burden of proving the amount of damages to a “reasonable certainty.” Plywood Oshkosh, Inc. v. Van’s Realty & Constr. of Appleton, Inc., 80 Wis.2d 26, 257 N.W.2d 847, 849 (1977) (“The claimant generally has the burden of proving by *179credible evidence to a reasonable certainty his damage, and the amount thereof must be established at least to a reasonable certainty.”)-10 Specifically, the District Court did not clearly err by finding that Banjo Buddies’ Exhibit 201 was insufficiently reliable. Further, the court did not commit legal error by refusing to estimate damages based on this unreliable exhibit, because Banjo Buddies could have, but failed to, introduce other, more reliable evidence as proof of the amount of damages.

To prove the amount of overcharge, Banjo Buddies combined two approaches. First, Banjo Buddies introduced invoices indicating Renosky’s costs for some components of the Banjo Minnow lure kit. The District Court accepted these invoices as reliable proof of Renosky’s costs. Banjo Buddies then added estimated overhead and a reasonable profit margin to arrive at the price Renosky should have charged for those components of the lure kit. However, these invoices only accounted for 20 of the 109 components of the Banjo Minnow lure kit. Banjo Buddies introduced Exhibit 201, an undated price quote from Reno-sky to a third party, National Media, to establish the prices Renosky should have charged Banjo Buddies and Tristar for the remaining 89 components. Combining the invoices (adjusted for overhead and profit) and the price quote, Banjo Buddies contends that Renosky should have charged Tristar and Banjo Buddies $3.44 per lure kit, $1.76 less than the amount actually charged, $5.20. The District Court, however, found the National Media price quote unreliable.

This finding was not clearly erroneous. First, the National Media quote is undated. There is evidence that over time some of Renosky’s component prices fell, while other component prices, operational expenses, and labor costs rose, after Reno-sky’s business manager produced the quote to Banjo Buddies that established the price of $5.20 per kit in March 1996. Given these fluctuating costs, the District Court properly observed that not knowing the date of the National Media quote makes it difficult to conclude that the component prices quoted therein should have been comparable to those in the Banjo Buddies quote. The District Court further noted that Banjo Buddies’ counsel failed to sufficiently question Renosky or his business manager about the National Media quote at trial. Such questioning could have readily established the date and context of the quote, and offered the persons most familiar with the component prices— Renosky and his business manager — an opportunity to explain the different prices in the National Media and Banjo Buddies price quotes. The National Media quote is not inherently unreliable, but given Banjo *180Buddies’ failure to substantiate the quote at trial, the District Court did not err by refusing to rely on the quote.11

Banjo Buddies alternatively argues that the District Court, having found liability, should nonetheless have estimated damages based on the less-than-reliable National Media price quote because it was the only available evidence. As the Wisconsin Supreme Court explained in Metropolitan Sewerage Comm’n v. R.W. Constr., Inc., 78 Wis.2d 451, 255 N.W.2d 293, 299 (1977), “where records are inadequate to assess specific damages, yet plaintiff has been injured ... and liability is clear,” “[i]t is enough if the evidence adduced is sufficient to enable a court or jury to make a fair and reasonable approximation.” (Internal citation omitted); see also Cutler Cranberry Co. v. Oakdale Elec. Co-op., 78 Wis.2d 222, 254 N.W.2d 234, 240 (1977) (“[T]he fact that the full extent of the damages is a matter of uncertainty by reason of the nature of the tort is not a ground for refusing damages.”). The problem here is that the lack of better evidence in this case is not due to a lack of adequate records, Metropolitan Sewerage, 255 N.W.2d at 299, or the “nature of the tort,” Cutler Cranberry, 254 N.W.2d at 240, but to Banjo Buddies’ failure to introduce more reliable evidence, either by introducing Renosky’s invoices for the remaining 89 components or substantiating the undated National Media quote through questioning at trial. As the court explained in Cutler Cranberry, the rule permitting estimated damages in the face of uncertainty as to the amount of damages “has been sustained where, from the nature of the case, the extent of injury and the amount of damage are not capable of exact and accurate proof.” Id. (emphasis added) (internal citation omitted).

Banjo Buddies attempts to lay the blame for its failure to introduce better evidence on Renosky. Banjo Buddies contends that Renosky failed to provide discovery “in a timely manner,” and did not produce “any invoices or other information on costs until two business days before trial.” However, Banjo Buddies never claims that Renosky ultimately failed to produce those documents. Further, if Banjo Buddies felt that Renosky had not complied (or not timely complied) with its discovery requests, it should have pursued relief under the discovery rules or sought a continuance. Banjo Buddies cannot reasonably claim that its burden of proof should be lowered because it did not have time to sift through the boxes of documents Renosky allegedly produced on the eve of trial. Furthermore, as noted above, see supra n. 11, Banjo Buddies’ failure to substantiate the National Media quote cannot be attributed to Renosky’s foot-dragging during discovery.

IV. Conclusion

For the reasons given above, we will affirm the District Court’s award of Reno-sky’s estimated profits on the Bionic Minnow project but reverse the District Court’s decision to add Renosky’s shareholder distributions to that amount. We *181will affirm the District Court’s judgment in all other respects.

******

Justice GORSUCH delivered the opinion of the Court.

*1494When it comes to remedies for trademark infringement, the Lanham Act authorizes many. A district court may award a winning plaintiff injunctive relief, damages, or the defendant's ill-gotten profits. Without question, a defendant's state of mind may have a bearing on what relief a plaintiff should receive. An innocent trademark violator often stands in very different shoes than an intentional one. But some circuits have gone further. These courts hold a plaintiff can win a profits remedy, in particular, only after showing the defendant willfully infringed its trademark. The question before us is whether that categorical rule can be reconciled with the statute's plain language.

The question comes to us in a case involving handbag fasteners. Romag sells magnetic snap fasteners for use in leather goods. Fossil designs, markets, and distributes a wide range of fashion accessories. Years ago, the pair signed an agreement allowing Fossil to use Romag's fasteners in Fossil's handbags and other products. Initially, both sides seemed content with the arrangement. But in time Romag discovered that the factories Fossil hired in China to make its products were using counterfeit Romag fasteners-and that Fossil was doing little to guard against the practice. Unable to resolve its concerns amicably, Romag sued. The company alleged that Fossil had infringed its trademark and falsely represented that its fasteners came from Romag. After trial, a jury agreed with Romag, and found that Fossil had acted "in callous disregard" of Romag's rights. At the same time, however, the jury rejected Romag's accusation that Fossil had acted willfully, as that term was defined by the district court.

For our purposes, the last finding is the important one. By way of relief for Fossil's trademark violation, Romag sought (among other things) an order requiring Fossil to hand over the profits it had earned thanks to its trademark violation. But the district court refused this request. The court pointed out that controlling Second Circuit precedent requires a plaintiff seeking a profits award to prove that the defendant's violation was willful. Not all circuits, however, agree with the Second Circuit's rule. We took this case to resolve that dispute over the law's demands. 588 U.S. ----, 139 S.Ct. 2778, 204 L.Ed.2d 1157 (2019).

Where does Fossil's proposed willfulness rule come from? The relevant section of the Lanham Act governing remedies for trademark violations, § 35, 60 Stat. 439-440, as amended, 15 U.S.C. § 1117(a), says this:

"When a violation of any right of the registrant of a mark registered in the Patent and Trademark Office, a violation under section 1125(a) or (d) of this title, or a willful violation under section 1125(c) of this title, shall have been established ..., the plaintiff shall be entitled, *1495subject to the provisions of sections 1111 and 1114 of this title, and subject to the principles of equity, to recover (1) defendant's profits, (2) any damages sustained by the plaintiff, and (3) the costs of the action."

Immediately, this language spells trouble for Fossil and the circuit precedent on which it relies. The statute does make a showing of willfulness a precondition to a profits award when the plaintiff proceeds under § 1125(c). That section, added to the Lanham Act some years after its initial adoption, creates a cause of action for trademark dilution-conduct that lessens the association consumers have with a trademark. But Romag alleged and proved a violation of § 1125(a), a provision establishing a cause of action for the false or misleading use of trademarks. And in cases like that, the statutory language has never required a showing of willfulness to win a defendant's profits. Yes, the law tells us that a profits award is subject to limitations found in §§ 1111 and 1114. But no one suggests those cross-referenced sections contain the rule Fossil seeks. Nor does this Court usually read into statutes words that aren't there. It's a temptation we are doubly careful to avoid when Congress has (as here) included the term in question elsewhere in the very same statutory provision.

A wider look at the statute's structure gives us even more reason for pause. The Lanham Act speaks often and expressly about mental states. Section 1117(b) requires courts to treble profits or damages and award attorney's fees when a defendant engages in certain acts intentionally and with specified knowledge . Section 1117(c) increases the cap on statutory damages from $200,000 to $2,000,000 for certain willful violations. Section 1118 permits courts to order the infringing items be destroyed if a plaintiff proves any violation of § 1125(a) or a willful violation of § 1125(c). Section 1114 makes certain innocent infringers subject only to injunctions. Elsewhere, the statute specifies certain mens rea standards needed to establish liability, before even getting to the question of remedies. See, e.g., §§ 1125(d)(1)(A)(i), (B)(i) (prohibiting certain conduct only if undertaken with "bad faith intent" and listing nine factors relevant to ascertaining bad faith intent). Without doubt, the Lanham Act exhibits considerable care with mens rea standards. The absence of any such standard in the provision before us, thus, seems all the more telling.

So how exactly does Fossil seek to conjure a willfulness requirement out of § 1117(a) ? Lacking any more obvious statutory hook, the company points to the language indicating that a violation under § 1125(a) can trigger an award of the defendant's profits "subject to the principles of equity." In Fossil's telling, equity courts historically required a showing of willfulness before authorizing a profits remedy in trademark disputes. Admittedly, equity courts didn't require so much in patent infringement cases and other arguably analogous suits. See, e.g., Dowagiac Mfg. Co. v. Minnesota Moline Plow Co. , 235 U.S. 641, 644, 650-651, 35 S.Ct. 221, 59 L.Ed. 398 (1915). But, Fossil says, trademark is different. There alone, a willfulness requirement was so long and universally recognized that today it rises to the level of a "principle of equity" the Lanham Act carries forward.

It's a curious suggestion. Fossil's contention that the term "principles of equity" includes a willfulness requirement would not directly contradict the statute's other, express mens rea provisions or render them wholly superfluous. But it would require us to assume that Congress intended to incorporate a willfulness requirement *1496here obliquely while it prescribed mens rea conditions expressly elsewhere throughout the Lanham Act. That might be possible, but on first blush it isn't exactly an obvious construction of the statute.

Nor do matters improve with a second look. The phrase "principles of equity" doesn't readily bring to mind a substantive rule about mens rea from a discrete domain like trademark law. In the context of this statute, it more naturally suggests fundamental rules that apply more systematically across claims and practice areas. A principle is a "fundamental truth or doctrine, as of law; a comprehensive rule or doctrine which furnishes a basis or origin for others." Black's Law Dictionary 1417 (3d ed. 1933); Black's Law Dictionary 1357 (4th ed. 1951). And treatises and handbooks on the "principles of equity" generally contain transsubstantive guidance on broad and fundamental questions about matters like parties, modes of proof, defenses, and remedies. See, e.g. , E. Merwin, Principles of Equity and Equity Pleading (1895); J. Indermaur & C. Thwaites, Manual of the Principles of Equity (7th ed. 1913); H. Smith, Practical Exposition of the Principles of Equity (5th ed. 1914); R. Megarry, Snell's Principles of Equity (23d ed. 1947). Our precedent, too, has used the term "principles of equity" to refer to just such transsubstantive topics. See, e.g., eBay Inc. v. MercExchange, L. L. C. , 547 U.S. 388, 391, 393, 126 S.Ct. 1837, 164 L.Ed.2d 641 (2006) ; Holmberg v. Armbrecht , 327 U.S. 392, 395, 66 S.Ct. 582, 90 L.Ed. 743 (1946). Congress itself has elsewhere used "equitable principles" in just this way: An amendment to a different section of the Lanham Act lists "laches, estoppel, and acquiescence" as examples of "equitable principles." 15 U.S.C. § 1069. Given all this, it seems a little unlikely Congress meant "principles of equity" to direct us to a narrow rule about a profits remedy within trademark law.

But even if we were to spot Fossil that first essential premise of its argument, the next has problems too. From the record the parties have put before us, it's far from clear whether trademark law historically required a showing of willfulness before allowing a profits remedy. The Trademark Act of 1905-the Lanham Act's statutory predecessor which many earlier cases interpreted and applied-did not mention such a requirement. It's true, as Fossil notes, that some courts proceeding before the 1905 Act, and even some later cases following that Act, did treat willfulness or something like it as a prerequisite for a profits award and rarely authorized profits for purely good-faith infringement. See, e.g., Horlick's Malted Milk Corp. v. Horluck's, Inc. , 51 F.2d 357, 359 (W.D. Wash. 1931) (explaining that the plaintiff "cannot recover defendant's profits unless it has been shown beyond a reasonable doubt that defendant was guilty of willful fraud in the use of the enjoined trade-name"); see also Saxlehner v. Siegel-Cooper Co. , 179 U.S. 42, 42-43, 21 S.Ct. 16, 45 L.Ed. 77 (1900) (holding that one defendant "should not be required to account for gains and profits" when it "appear[ed] to have acted in good faith"). But Romag cites other cases that expressly rejected any such rule. See, e.g., Oakes v. Tonsmierre , 49 F. 447, 453 (C.C.S.D. Ala. 1883) ; see also Stonebraker v. Stonebraker , 33 Md. 252, 268 (1870) ; Lawrence-Williams Co. v. Societe Enfants Gombault et Cie , 52 F.2d 774, 778 (C.A.6 1931).

The confusion doesn't end there. Other authorities advanced still different understandings about the relationship between mens rea and profits awards in trademark cases. See, e.g., H. Nims, Law of Unfair Competition and Trade-Marks § 424 (2d ed. 1917) ("An accounting will not be ordered where the infringing party acted innocently and in ignorance of the plaintiff's *1497rights"); N. Hesseltine, Digest of the Law of Trade-Marks and Unfair Trade 305 (1906) (contrasting a case holding "[n]o account as to profits allowed except as to user after knowledge of plaintiff's right to trademark" and one permitting profits "although defendant did not know of infringement" (emphasis added)). And the vast majority of the cases both Romag and Fossil cite simply failed to speak clearly to the issue one way or another. See, e.g., Hostetter v. Vowinkle , 12 F.Cas. 546, 547 (No. 6,714) (C.C.D. Neb. 1871) ; Graham v. Plate , 40 Cal. 593, 597-599 (1871) ; Hemmeter Cigar Co. v. Congress Cigar Co. , 118 F.2d 64, 71-72 (C.A.6 1941).

At the end of it all, the most we can say with certainty is this. Mens rea figured as an important consideration in awarding profits in pre-Lanham Act cases. This reflects the ordinary, transsubstantive principle that a defendant's mental state is relevant to assigning an appropriate remedy. That principle arises not only in equity, but across many legal contexts. See, e.g., Smith v. Wade , 461 U.S. 30, 38-51, 103 S.Ct. 1625, 75 L.Ed.2d 632 (1983) ( 42 U.S.C. § 1983 ); Morissette v. United States , 342 U.S. 246, 250-263, 72 S.Ct. 240, 96 L.Ed. 288 (1952) (criminal law); Wooden-Ware Co. v. United States , 106 U.S. 432, 434-435, 1 S.Ct. 398, 27 L.Ed. 230 (1882) (common law trespass). It's a principle reflected in the Lanham Act's text, too, which permits greater statutory damages for certain willful violations than for other violations. 15 U.S.C. § 1117(c). And it is a principle long reflected in equity practice where district courts have often considered a defendant's mental state, among other factors, when exercising their discretion in choosing a fitting remedy. See, e.g., L. P. Larson, Jr., Co. v. Wm. Wrigley, Jr., Co. , 277 U.S. 97, 99-100, 48 S.Ct. 449, 72 L.Ed. 800 (1928) ; Lander v. Lujan , 888 F.2d 153, 155-156 (C.A.D.C. 1989) ; United States v. Klimek , 952 F.Supp. 1100, 1117 (E.D. Pa. 1997). Given these traditional principles, we do not doubt that a trademark defendant's mental state is a highly important consideration in determining whether an award of profits is appropriate. But acknowledging that much is a far cry from insisting on the inflexible precondition to recovery Fossil advances.

With little to work with in the statute's language, structure, and history, Fossil ultimately rests on an appeal to policy. The company tells us that stouter restraints on profits awards are needed to deter "baseless" trademark suits. Meanwhile, Romag insists that its reading of the statute will promote greater respect for trademarks in the "modern global economy." As these things go, amici amplify both sides' policy arguments. Maybe, too, each side has a point. But the place for reconciling competing and incommensurable policy goals like these is before policymakers. This Court's limited role is to read and apply the law those policymakers have ordained, and here our task is clear. The judgment of the court of appeals is vacated, and the case is remanded for further proceedings consistent with this opinion.

It is so ordered.

Justice ALITO, with whom Justice BREYER and Justice KAGAN join, concurring.

We took this case to decide whether willful infringement is a prerequisite to an award of profits under 15 U.S.C. § 1117(a). The decision below held that willfulness is such a prerequisite. App. to Pet. for Cert. 32a. That is incorrect. The relevant authorities, particularly pre-Lanham Act case law, show that willfulness is a highly important consideration in awarding profits under § 1117(a), but not an absolute precondition. I would so hold and concur on that ground.

Justice SOTOMAYOR, concurring in the judgment.

*1498I agree that 15 U.S.C. § 1117(a) does not impose a "willfulness" prerequisite for awarding profits in trademark infringement actions. Courts of equity, however, defined "willfulness" to encompass a range of culpable mental states-including the equivalent of recklessness, but excluding "good faith" or negligence. See 5 McCarthy on Trademarks and Unfair Competition § 30:62 (5th ed. 2019) (explaining that "willfulness" ranged from fraudulent and knowing to reckless and indifferent behavior); see also, e.g., Lawrence-Williams Co. v. Societe Enfants Gombault et Cie , 52 F.2d 774, 778 (C.A.6 1931) ; Regis v. Jaynes , 191 Mass. 245, 248-249, 77 N.E. 774, 776 (1906).

The majority suggests that courts of equity were just as likely to award profits for such "willful" infringement as they were for "innocent" infringement. Ante , at 1496 - 1497. But that does not reflect the weight of authority, which indicates that profits were hardly, if ever, awarded for innocent infringement. See, e.g., Wood v. Peffer , 55 Cal.App.2d 116, 125, 130 P.2d 220 (1942) (explaining that "equity constantly refuses, for want of fraudulent intent, the prayer for an accounting of profits"); Globe-Wernicke Co. v. Safe-Cabinet Co. , 110 Ohio St. 609, 617, 144 N.E. 711, 713 (1924) ("By the great weight of authority, particularly where the infringement ... was deliberate and willful, it is held that the wrongdoer is required to account for all profits realized by him as a result of his wrongful acts"); Dickey v. Mutual Film Corp. , 186 A.D. 701, 702, 174 N.Y.S. 784 (1919) (declining to award profits because there was "no proof of any fraudulent intent upon the part of the defendant"); Standard Cigar Co. v. Goldsmith , 58 Pa.Super. 33, 37 (1914) (reasoning that a defendant "should be compelled to account for ... profits" where "the infringement complained of was not the result of mistake or ignorance of the plaintiff 's right"). Nor would doing so seem to be consistent with longstanding equitable principles which, after all, seek to deprive only wrongdoers of their gains from misconduct. Cf. Duplate Corp. v. Triplex Safety Glass Co. , 298 U.S. 448, 456-457, 56 S.Ct. 792, 80 L.Ed. 1274 (1936). Thus, a district court's award of profits for innocent or good-faith trademark infringement would not be consonant with the "principles of equity" referenced in § 1117(a) and reflected in the cases the majority cites. Ante at 1496 - 1497.

Because the majority is agnostic about awarding profits for both "willful" and innocent infringement as those terms have been understood, I concur in the judgment only.