RIPPLE, Circuit Judge.
In this appeal, we review the district court’s award of damages for the infringement of a federally registered trademark. [1342] We reversed the district court’s first award. Sands, Taylor & Wood v. Quaker Oats Co., 978 F.2d 947 (7th Cir.1992) (“Sands I"), cert. denied, — U.S. -, 113 S.Ct. 1879, 123 L.Ed.2d 497 (1993). The district court redetermined the plaintiffs damages and entered judgment in favor of the plaintiff for $20,656,-822. The court also awarded prejudgment interest, calculated from that portion of the verdict representing a reasonable royalty, in the amount of $5,431,413. For the reasons that follow, we affirm in part and vacate in part the judgment of the district court and remand for further proceedings.
I
BACKGROUND
A. Earlier Proceedings
The details of this litigation are recounted fully in our first opinion. Sands I, 978 F.2d at 949-51. We therefore set forth below only those facts essential to the resolution of issues before us and refer the reader to our earlier opinion for additional details.
In 1984, Sands, Taylor & Wood (“STW”) brought suit against The Quaker Oats Company (“Quaker”) for violations of the Lanham Act, 15 U.S.C. § 1051. It alleged that Quaker was infringing STW’s trademark, “Thirst-Aid,” in a nationally-televised commercial advertising campaign promoting Quaker’s isotonic beverage, “Gatorade.” Quaker continued using the mark until 1990, when, after a bench trial, the district court ruled that Quaker’s use was infringing STW’s trademark. The district court awarded STW 10% of Quaker’s pre-tax profits on Gatorade for the period during which Quaker used Thirsts Aid in its advertising campaign. This award of profits amounted to $31,392,493. The court also awarded STW attorneys’ fees and costs as well as prejudgment interest.
In its first opinion, the district court examined the types of relief that it could award under the Lanham Act. The district court first determined that STW was entitled to profits. It noted, however, that forcing Quaker to disgorge all of its profits from the sales of Gatorade during the period of infringement might overcompensate STW:
Defendant’s profits may be significantly disproportionate to plaintiffs circumstances, such that an award of profits may represent punishment to the defendant (as opposed to compensation for the plaintiff), and unjustifiable enrichment and a windfall to the plaintiff. Therefore, the amount of profits to be awarded should be related to the financial benefit received because of the unlawful use of the mark.
Appellant’s App. at 106a (citations omitted). The district court therefore attempted to assess that portion of Quaker’s profits attributable to the Thirst-Aid mark. In its analysis, it rejected the opinion of Dr. William Lynk, Quaker’s 'expert, that the Thirst>-Aid mark had little to do with Gatorade’s success:
We find Dr. Lynk’s testimony of little value in estimating the financial benefits defendant gained from the Thirst Aid Campaign. While admittedly the Thirst Aid campaign is not the sole cause of Gatorade’s success, the defendant’s substantial and continuous commitment to the campaign suggests that the Thirst Aid message is a valuable component in Gatorade’s overall marketing effort.
Id. at 107a. Believing that at least a portion of the profits could be attributed to Quaker’s illegal use of the mark, it concluded:
Many factors have contributed to Gatorade’s success. But, it is reasonable to infer that defendant’s aggressive THIRST-AID advertising campaign was responsible for 10% of the product’s success and hence profits. Defendant’s profits on Gatorade sales were 247.3 million dollars. Accordingly, we award plaintiff $24,730,000.00 (10% of defendant’s before tax profits) for defendant’s willful infringement of plaintiffs mark and to prevent defendant’s unjust enrichment from its use.
Id. at 108a (citations omitted).
The district court then considered and dismissed as inappropriate other forms of monetary relief. With regard to actual damages, the court found that STW had not presented any evidence of lost profits or sales. It rejected STW’s argument that its licensing proposals to other major companies, refused [1343] by those firms because of the Gatorade campaign, resulted in actual damage:
We reject both proposals as evidence of plaintiffs actual damage- Both proposals represent conjectural lost business opportunities which may or may not have proceeded but for defendant’s advertising. We fail to see how these lost opportunities constitute actual harm justifying a damage award separate from defendants’ profits.
Id. at 109a. The court similarly found an award for corrective advertising inappropriate. Corrective advertising awards, explained the court, have been used “to restore plaintiffs reputation to its former level via an actual reparative advertising campaign.” Id. at 110a. Because STW had not made concurrent use of the Thirst-Aid mark, there was no need to counteract Quaker’s advertising.
Finally, the court rejected an award of a reasonable royalty. The cases STW had relied on to support such an award, held the court, were inapposite because in those cases there had been actual negotiations between the parties to serve as a basis for an award of a reasonable royalty. By contrast,
[t]he parties in this case never considered a licensing agreement. Thus, any measure of damages based upon a royalty would force the court to engage in a hypothetical inquiry into what would have been a reasonable royalty for the defendant to pay plaintiff had the parties contemplated a royalty arrangement. Damages predicated on a speculative royalty rate are clearly inappropriate.
Id. at 112a. Quaker appealed to this court.
On that appeal, we affirmed the judgment of the district court insofar as it found Quaker’s use of the Thirst-Aid mark to be infringing, but we vacated the district court’s monetary award which was based on Quaker’s profits on Gatorade. On the question of damages, we directed that the district court apply the following guiding principles on remand:
(1) the court may not simply award STW a percentage of Quaker’s profits; (2) the court should use a reasonable royalty as a baseline or starting point for determining the appropriate award; (3) in determining the appropriate award, the court may take into account the possible need for deterrence, which may involve consideration of the amount of Quaker’s profits.
Sands I, 978 F.2d at 963 n. 19.
B. The Recalculation of STW’s Damages
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RIPPLE, Circuit Judge.
In this appeal, we review the district court’s award of damages for the infringement of a federally registered trademark. [1342] We reversed the district court’s first award. Sands, Taylor & Wood v. Quaker Oats Co., 978 F.2d 947 (7th Cir.1992) (“Sands I"), cert. denied, — U.S. -, 113 S.Ct. 1879, 123 L.Ed.2d 497 (1993). The district court redetermined the plaintiffs damages and entered judgment in favor of the plaintiff for $20,656,-822. The court also awarded prejudgment interest, calculated from that portion of the verdict representing a reasonable royalty, in the amount of $5,431,413. For the reasons that follow, we affirm in part and vacate in part the judgment of the district court and remand for further proceedings.
I
BACKGROUND
A. Earlier Proceedings
The details of this litigation are recounted fully in our first opinion. Sands I, 978 F.2d at 949-51. We therefore set forth below only those facts essential to the resolution of issues before us and refer the reader to our earlier opinion for additional details.
In 1984, Sands, Taylor & Wood (“STW”) brought suit against The Quaker Oats Company (“Quaker”) for violations of the Lanham Act, 15 U.S.C. § 1051. It alleged that Quaker was infringing STW’s trademark, “Thirst-Aid,” in a nationally-televised commercial advertising campaign promoting Quaker’s isotonic beverage, “Gatorade.” Quaker continued using the mark until 1990, when, after a bench trial, the district court ruled that Quaker’s use was infringing STW’s trademark. The district court awarded STW 10% of Quaker’s pre-tax profits on Gatorade for the period during which Quaker used Thirsts Aid in its advertising campaign. This award of profits amounted to $31,392,493. The court also awarded STW attorneys’ fees and costs as well as prejudgment interest.
In its first opinion, the district court examined the types of relief that it could award under the Lanham Act. The district court first determined that STW was entitled to profits. It noted, however, that forcing Quaker to disgorge all of its profits from the sales of Gatorade during the period of infringement might overcompensate STW:
Defendant’s profits may be significantly disproportionate to plaintiffs circumstances, such that an award of profits may represent punishment to the defendant (as opposed to compensation for the plaintiff), and unjustifiable enrichment and a windfall to the plaintiff. Therefore, the amount of profits to be awarded should be related to the financial benefit received because of the unlawful use of the mark.
Appellant’s App. at 106a (citations omitted). The district court therefore attempted to assess that portion of Quaker’s profits attributable to the Thirst-Aid mark. In its analysis, it rejected the opinion of Dr. William Lynk, Quaker’s 'expert, that the Thirst>-Aid mark had little to do with Gatorade’s success:
We find Dr. Lynk’s testimony of little value in estimating the financial benefits defendant gained from the Thirst Aid Campaign. While admittedly the Thirst Aid campaign is not the sole cause of Gatorade’s success, the defendant’s substantial and continuous commitment to the campaign suggests that the Thirst Aid message is a valuable component in Gatorade’s overall marketing effort.
Id. at 107a. Believing that at least a portion of the profits could be attributed to Quaker’s illegal use of the mark, it concluded:
Many factors have contributed to Gatorade’s success. But, it is reasonable to infer that defendant’s aggressive THIRST-AID advertising campaign was responsible for 10% of the product’s success and hence profits. Defendant’s profits on Gatorade sales were 247.3 million dollars. Accordingly, we award plaintiff $24,730,000.00 (10% of defendant’s before tax profits) for defendant’s willful infringement of plaintiffs mark and to prevent defendant’s unjust enrichment from its use.
Id. at 108a (citations omitted).
The district court then considered and dismissed as inappropriate other forms of monetary relief. With regard to actual damages, the court found that STW had not presented any evidence of lost profits or sales. It rejected STW’s argument that its licensing proposals to other major companies, refused [1343] by those firms because of the Gatorade campaign, resulted in actual damage:
We reject both proposals as evidence of plaintiffs actual damage- Both proposals represent conjectural lost business opportunities which may or may not have proceeded but for defendant’s advertising. We fail to see how these lost opportunities constitute actual harm justifying a damage award separate from defendants’ profits.
Id. at 109a. The court similarly found an award for corrective advertising inappropriate. Corrective advertising awards, explained the court, have been used “to restore plaintiffs reputation to its former level via an actual reparative advertising campaign.” Id. at 110a. Because STW had not made concurrent use of the Thirst-Aid mark, there was no need to counteract Quaker’s advertising.
Finally, the court rejected an award of a reasonable royalty. The cases STW had relied on to support such an award, held the court, were inapposite because in those cases there had been actual negotiations between the parties to serve as a basis for an award of a reasonable royalty. By contrast,
[t]he parties in this case never considered a licensing agreement. Thus, any measure of damages based upon a royalty would force the court to engage in a hypothetical inquiry into what would have been a reasonable royalty for the defendant to pay plaintiff had the parties contemplated a royalty arrangement. Damages predicated on a speculative royalty rate are clearly inappropriate.
Id. at 112a. Quaker appealed to this court.
On that appeal, we affirmed the judgment of the district court insofar as it found Quaker’s use of the Thirst-Aid mark to be infringing, but we vacated the district court’s monetary award which was based on Quaker’s profits on Gatorade. On the question of damages, we directed that the district court apply the following guiding principles on remand:
(1) the court may not simply award STW a percentage of Quaker’s profits; (2) the court should use a reasonable royalty as a baseline or starting point for determining the appropriate award; (3) in determining the appropriate award, the court may take into account the possible need for deterrence, which may involve consideration of the amount of Quaker’s profits.
Sands I, 978 F.2d at 963 n. 19.
B. The Recalculation of STW’s Damages
The district court’s first step on remand was to determine a reasonable royalty rate for the Thirst-Aid mark. The court assumed that this figure should be based on Quaker’s yearly Gatorade sales, excluding for each year of infringement the pre-infringement sales level of $95 million. R. 401 at 10. To determine a reasonable royalty, the court considered what a hypothetical negotiation for the right to license the Thirst-Aid mark would yield. First, it noted that the Thirsts Aid mark had proven a successful marketing tool when another company, Pet, Inc., test-marketed an isotonic beverage in 1980. Second, the court observed that Gatorade’s sales had slumped prior to Quaker’s infringement and therefore that Quaker was in need of a new marketing approach for the product. Third, it noted that Quaker had considered the proposed advertising campaign based on the Thirst-Aid mark to be superior to the alternatives. Fourth, the court considered STW’s proposed rate of 1% for the first year of infringement and .5% for each subsequent year of infringement. The court compared this proposed rate with expert testimony adduced at trial regarding a reasonable rate for the Thirst-Aid mark.1 It also compared this proposed rate with other royalty rates for trademark licenses and found it smaller, except for the rate Pet paid for its brief use of the Thirst-Aid mark in 1980, which was a flat fee of $10,000 plus a .5% running royalty on sales for the first ten months and thereafter .33% of sales. Finally, the court considered, but found unpersuasive, Quaker’s position [1344] that a flat fee of $100,000 would exceed the fair market value of the Thirst>-Aid mark in 1984.
After discussing the above considerations, the court decided to use STW’s proposed royalty rate of 1% for the first year of infringement and .5% for each successive year of infringement. Applying this rate to Quaker’s sales of Gatorade during the period of infringement (minus the pre-infringement sales level), the court calculated the baseline royalty to be $10,328,411. R.401 at 15. In determining this rate, the court said that it had considered
plaintiffs prior licenses, (defendant has declined to disclose its prior licenses), plaintiffs licensing policies, the nature and scope of defendant’s infringing use ... the special value of THIRST-AID to defendant in 1984 (the huge increase in sales during infringement followed by a sharp decline after infringement ceased), the profitability of the defendant’s infringement, the questionable attractiveness of defendant’s alternatives, the expert opinions and defendant’s persistent infringement in the face of the admonitions by its inside and outside counsel and my May 1985 ruling that it was infringing.
Id. at 14-15. It also noted that its determination was merely an “ ‘attempt to measure the value to the infringer,’ ” id. at 10 (quoting James M. Koelmay, Monetary Relief for Trademark Infringement Under the Lan-ham Act, 72 Trademark Rptr. 459, 544 (1982)) (emphasis added), and necessarily involved speculation, id.
Having established as a baseline a reasonable royalty of over $10 million, the court then addressed whether the award ought to be enhanced. It posed the question in the following terms:
Will the imposition of a hypothetical licensing royalty deter predatory conduct such as defendant’s? I doubt it. The royalty is nothing more than an approximation of what defendant would have paid plaintiff had defendant acted lawfully. “[An] in-fringer [has] nothing to lose, and everything to gain if [it] could count on paying only the normal, routine royalty, nonin-fringers might have paid ... [T]he infringer would be in a ‘heads-I-win, tails-you-lose position.’ ” Panduit Corp. v. Stahlin [Bros.] Fibre Works, 575 F.2d 1152, 1158 (6th Cir.1978).
R.401 at 15-16. The court decided that “[t]o deter conduct such as defendant’s,” id. at 17, it would double the amount of the hypothetical royalty from $10,328,411 to $20,656,822. The court added $5,431,413 in prejudgment interest to the baseline portion of the award.2 The final sum was therefore $26,088,235 (compared to the original award of $41,996,-680, when factoring the same components). The court also awarded over $400,000 in attorneys’ fees and expenses; these fees and expenses are not disputed on appeal.
II
DISCUSSION
Although the appellant’s brief invites us, directly and by suggestion, to address a number of issues already settled at earlier stages of this litigation — a tactic that has detracted substantially from the overall helpfiilness of the brief — we emphatically decline to revisit those issues. The only issue before us in this appeal is whether the judgment under review conforms with our earlier decision and the governing principles of law embodied in that decision.
A. Calculation of the Royalty Rate
We turn first to the district court’s calculation of the royalty.3 The district court accepted STW’s proposed hypothetical royal[1345] ty rate of 1% of Gatorade sales, minus preinfringement sales levels, for the first year of infringement, and .5% for each year of infringement thereafter. We are convinced that the district court committed no reversible error in deciding upon this valuation, and that this rate is in accord with our mandate in Sands I that the district court calculate a “reasonable royalty.” 978 F.2d at 963 n. 19. Nevertheless, for the sake of completeness, we shall address the main arguments presented to us on appeal.4
Quaker contends that the royalty is not reasonable because the l%-.5% rate is almost double the rate paid by Pet, which licensed the Thirst-Aid mark in 1980. However, the record contains evidence that the value of the Thirst-Aid mark was higher in 1984 than in 1980, thus justifying a rate in 1984 higher than that paid by Pet in 1980. In 1980, the Thirst-Aid mark had not been used in connection with an isotonic beverage; in that context, the mark was untested and unproven. Pet’s experience showed that the mark had promise: In a four-month period, Pet’s beverage captured 25% of the isotonic beverage market in the test area. In addition, we must consider Quaker’s need for the mark. In 1984, the time of the hypothetical negotiation contemplated by the district court, Quaker was about to launch a national advertising campaign based on the Thirsts Aid mark. If it had failed to secure the right to use the mark, then it would have had to use one of its alternative advertising campaigns. Consumer testing revealed that the Thirst-Aid campaign was the best of the options available to Quaker. See J.A. 1643-56, 2677-78. (As we shall discuss below at greater length, these variables injected significant ambiguity into the royalty calculation. Nevertheless, they could not be ignored and the district court was entitled to consider them.) We also note that the rate selected by the district court was substantially lower than the rate used by STW for some other licensing ventures and lower than that suggested by its own expert witness. See J.A. at 766-68.5 We conclude that the district court did not err in calculating a reasonably royalty of $10,328,411.6
B. Enhancement of the Reasonable Royalty
1.
Sands I directed the district court to “use a reasonable royalty as a baseline or starting point for determining the appropriate award.” 978 F.2d at 963 n. 19. We then stated that “in determining the appropriate award, the court may take into account the possible need for deterrence, which may involve consideration of the amount of Quak[1346] er’s profits.” Id. On remand, the district court explicitly considered whether it should award more than the approximately $10 million for the reasonable royalty:
Is this award adequate? Defendant knowingly and in bad faith infringed plaintiffs incontestable mark. Defendant knew of the mark. It knew of its registration. It knew it was incontestable. It knew that it had been used successfully by Pet. It was told immediately following its public use that it was infringing and would damage plaintiffs mark. It disregarded the advice of its outside trademark counsel to minimize its use of THIRST-AID in its advertising. It persisted for five years in its infringing use of plaintiffs THIRST-AID mark after I ruled in June, 1985 that its use was infringing.