
551 F.3d 65 (2008)
VISIBLE SYSTEMS CORPORATION, Plaintiff, Appellant/Cross-Appellee,
v.
UNISYS CORPORATION, Defendant, Appellee/Cross-Appellant.
Nos. 07-2730, 08-1410, 08-1411.
United States Court of Appeals, First Circuit.
Heard November 3, 2008.
Decided December 23, 2008.
*68 Stephen H. Galebach for appellant/cross-appellee.
William L. Boesch with whom Anthony M. Doniger and Sugarman, Rogers, Barshak & Cohen, P.C. were on brief for appellee/cross-appellant.
Before LYNCH, Chief Judge, BOUDIN and STAHL, Circuit Judges.
LYNCH, Chief Judge.
A jury awarded Visible Systems Corporation ("VSC") trademark infringement damages of $250,000 against Unisys Corporation on a reverse confusion claim. See 15 U.S.C. § 1125(a). The district court also issued a permanent injunction prohibiting Unisys from using the trademarks or service marks 3D VISIBLE ENTERPRISE, 3D-VE, or VISIBLE in the United States in the enterprise modeling or enterprise architecture fields.
VSC appeals, asserting it was entitled to more. Its primary argument is that the trial judge erred in not granting it a jury trial under both the Lanham Act and the Seventh Amendment on its claim for an accounting of Unisys' profits. This court has not considered before the question of whether there is a jury trial right on such a claim. VSC also argues the court erred in tailoring the injunction too narrowly and in denying VSC its attorneys' fees.
*69 Unisys cross-appeals, arguing the evidence was insufficient to support both the jury's finding of infringement and the damages awarded.
We reject all of the challenges and affirm, leaving the parties where they were.

I.
Because the case presents sufficiency of the evidence arguments, we state the facts taking all inferences in favor of the jury verdict. See Valentín-Almeyda v. Municipality of Aguadilla, 447 F.3d 85, 95-96 (1st Cir.2006).
VSC is a small Massachusetts company with less than two dozen employees, founded in 1984, which primarily sells software products in the enterprise modeling and enterprise architecture field. "Enterprise modeling" and "enterprise architecture" involve the diagraming of an entity's business to demonstrate relationships between information flow and business processes and to allow decisionmakers to identify errors or redundancies. VSC provides its customers modeling tools, or software, that diagram their organizations and automatically generate productivity-improving software programs. VSC's modeling tools provide value by aiding clients' decisionmaking and by reducing the need to hand-code productivity-improving software, resulting in decreased costs and errors.
VSC sells its software products to private corporations and government agencies. Purchasing decisions are largely made by sophisticated IT professionals within those organizations. The company's primary marketing channels involve sales of modeling tools through downloads from its website, www.visible.com. VSC's modeling products, by the mid-1990s, were the second most widely used modeling tools in university IT-related courses.
VSC also provided staff-based consulting services from approximately 1985 to 2002. VSC moved in 2002 to using part-time consultants and on-call, temporary subcontractors. Consulting is a much smaller part of VSC's business than the sale of software. Some 80 to 90% of VSC's revenue comes from software sales. Its consulting customers contract with VSC for mentoring and training; significantly, this is only done on VSC's modeling software. Representative clients include the Arizona state court system, which contracted with VSC to upgrade its information technology system.
In 1997, VSC acquired a company started by Clive Finkelstein, known as the father of information engineering. The products and services of his company took on the Visible name, and his association led to greater prominence for the name.
VSC registered the mark VISIBLE SYSTEMS in 1985 for its enterprise modeling software. It registered the additional trademark VISIBLE in 2001 for its software and registered the service mark VISIBLE for its training and consulting services, "namely providing advice in the field of information technology."
Unisys, the defendant, was formed in 1986 by the merger of two leading manufacturers of mainframe computers. Unisys is a much larger company than VSC, employing about 30,000 people worldwide. Since the mid-1990s, Unisys has focused on providing services, particularly consulting, rather than products. Unisys' customers include government organizations and private firms, such as airlines and telecommunications companies. Part of Unisys' consulting methodology involves creating virtual models of clients' information systems to identify problems and solutions.
Although Unisys does not develop software, its consultants use modeling *70 tool software in many of their engagements. Unisys consultants use software from third-party providers, such as IBM and Proforma, and are "tool agnostic," meaning that Unisys' consultants use the software the client desires if the client expresses a preference. Unisys also occasionally sells software products to its consulting clients or to purchasers of its mainframes. These are mainly not Unisys-developed products.
On June 17, 2004, Unisys launched a marketing campaign under the mark 3D VISIBLE ENTERPRISE with an advertisement in the Wall Street Journal. Unisys filed for registration in April 2004. Its attempt to register the mark was put on hold pending resolution of this case. Under the 3D VISIBLE ENTERPRISE mark, Unisys sold consulting services to assist clients with enterprise modeling. The campaign also included sales of third-party modeling software to Unisys' consulting clients as part of its consulting services. In addition to using the term "visible" in its formal 3D VISIBLE ENTERPRISE mark, Unisys used the term in marketing communications that included phrases such as "Visible Breakthrough," "Visible Commerce," and "Visible Advantage."
VSC sued Unisys in federal district court on May 3, 2005, under the Lanham Act and state law, seeking damages, an accounting of Unisys' profits, and injunctive relief.[1] Unisys continued to use marks such as VISIBLE ADVANTAGE after suit was filed.
Before trial, the court denied Unisys' motion for summary judgment. The court then held that there was no evidence that Unisys adopted its mark in bad faith; it later granted Unisys' motion in limine to preclude evidence and argument on the issue of bad faith. At the charge conference after the close of VSC's evidence and just before the end of trial, VSC sought a jury instruction that the jury consider the remedy of an accounting of defendant's profits. The court refused, noting that VSC had "had the option of taking that route, but ... didn't." The court held the issue was for the court and said that in any event, the evidence was insufficient to support such a remedy. The court stated "if [the jury] ever came back with a verdict, I would have to throw it out."
At trial, VSC opted to present its case to the jury on a reverse confusion theory of recovery. VSC's theory was that Unisys had saturated the market with a mark substantially similar to VSC's trademarks, leading potential customers to believe that Unisys had acquired VSC. This confusion resulted in lost sales to VSC of software and services. VSC also presented some damages evidence that the parties competed in the sale of consulting services, and that Unisys' appropriation of the VISIBLE mark for its own services caused VSC harm in the consulting portion of VSC's business. However, a VSC witness testified that while VSC's software sales had declined after Unisys' infringement, VSC's consulting sales had increased.
With no objection from VSC, the court instructed the jury that VSC claimed Unisys had "advertised and promoted the 3D Visible Enterprise name in a way that has so saturated the market that potential customers are likely to be misled into thinking that Visible Systems' goods, in fact, originate from Unisys." The special questions to the jury specifically included VSC's "products and/or services."
*71 Unisys moved for judgment as a matter of law at the close of VSC's case, arguing that the evidence was insufficient to conclude that VSC had a protectable right to use the mark VISIBLE, that there was a likelihood of confusion between Unisys' and VSC's marks, or that VSC was entitled to an accounting of Unisys' profits as a remedy. See Fed.R.Civ.P. 50, 52. The court reserved its ruling.
The jury found in favor of VSC on special questions that:
[1.] Visible Systems Corporation established a right to a trademark in the word VISIBLE[;]
[2.] ... [T]he Unisys 3D VISIBLE ENTERPRISE mark is substantially similar to Visible Systems VISIBLE mark[;]
[3.] Visible Systems established the likelihood that potential customers have been or will be confused into mistakenly believing that Unisys Corporation is the source or sponsor of Visible Systems' products and/or services; ... [; and]
[4.] Unisys Corporation's infringement of Visible Systems' mark [was] willful.
The jury awarded VSC $250,000 in damages.
After the verdict, VSC moved for, among other things, a permanent injunction, attorneys' fees, and a supplementary jury trial to determine an award of Unisys' profits or in the alternative an award of $100 million of Unisys' profits. Unisys filed a renewed motion for judgment as a matter of law, arguing that the evidence was insufficient to support the jury's finding of infringement, its award of damages, or its finding of willfulness. The court denied Unisys' motion. Unisys also filed a memorandum asking the court to adopt injunctive relief which was more limited than VSC's request. The court issued an injunction similar in scope to Unisys' proposal. The court denied VSC's request for attorneys' fees, concluding that the case was not an "exceptional case" within the meaning of the Lanham Act. The court again declined VSC's request for an accounting of Unisys' profits, saying it considered that the issue was for the court and that, in any event, the evidence was insufficient to support such an award.

II.

UNISYS' APPEAL FROM THE VERDICT AND FROM THE DAMAGES AWARD

A. Sufficiency of Evidence to Support the Jury Infringement Finding

Unisys argues that the facts did not support the jury finding that Unisys had infringed VSC's marks. Importantly, there is no challenge to the jury instructions on infringement or to the jury findings of VSC's right to a trademark and of substantial similarity.
Unisys contests only the finding of likelihood of confusion. Our review of the denial of Unisys' renewed motion for judgment as a matter of law under Fed. R.Civ.P. 50(b) is de novo. See Valentín-Almeyda, 447 F.3d at 95. The underlying standard for grant of a Rule 50(b) motion is much more deferential to the verdict. See id. at 95-96. A motion for judgment as a matter of law may be granted only if a reasonable person, on the evidence presented, could not reach the conclusion that the jury reached. See Attrezzi, LLC v. Maytag Corp., 436 F.3d 32, 37 (1st Cir. 2006).
VSC chose to present this case to the jury as a reverse confusion case. Under the classic "forward confusion" theory, a trademark holder alleges customers will purchase goods from the infringing junior user (here, Unisys) under the mistaken belief that they are purchasing from the *72 senior user (here, VSC). See 4 J. McCarthy, McCarthy on Trademarks and Unfair Competition § 23:10, at 23-46 (4th Ed.2006); see also Boston Duck Tours, LP v. Super Duck Tours, LLC, 531 F.3d 1, 12 (1st Cir.2008).
By contrast, under a reverse confusion theory, customers purchase the senior user's goods under the "misimpression that the junior user is the source of the senior user's goods. ... [C]onsumers may consider [the senior user] the unauthorized infringer, and [the junior user's] use of the mark may in that way injure [the senior user's] reputation and impair its goodwill." 4 McCarthy, supra, § 23:10, at 23-47 (alterations and omission in original) (quoting Banff, Ltd. v. Federated Dep't Stores, Inc., 841 F.2d 486, 490 (2d Cir.1988)) (internal quotation mark omitted); see also Attrezzi, 436 F.3d at 38-39; Pignons S.A. de Mecanique de Precision v. Polaroid Corp., 657 F.2d 482, 492 n. 4 (1st Cir.1981). Harm from the reverse confusion may occur because the junior user "saturates the market" and overwhelms the senior user, causing harm to the value of the trademark and the senior user's business.[2]Attrezzi, 436 F.3d at 39. "A reverse confusion case is proven only if the evidence shows that the junior user was able to swamp the reputation of the senior user with a relatively much larger advertising campaign." 4 McCarthy, supra, § 23:10, at 23-47 to -48. There is no actionable reverse confusion in the absence of a showing of likely confusion as to source or sponsorship. See DeCosta v. Viacom Int'l, Inc., 981 F.2d 602, 609 (1st Cir.1992). A trademark holder must show a likelihood of confusion; it need not show actual confusion, but actual confusion will strengthen the holder's infringement claim. Borinquen Biscuit Corp. v. M.V. Trading Corp., 443 F.3d 112, 120 (1st Cir.2006).
On the evidence, VSC's strongest case for likelihood of confusion was as follows. VSC was a small company, firmly entrenched in what was once, in 1985, the new field of enterprise modeling. Indeed, VSC became associated with the academic progenitor in the field, Clive Finkelstein, who founded a company which VSC acquired and who served as VSC's Chief Scientist. The term "VISIBLE" was VSC's mark, and it was used to denote VSC's various software products. For many years, VSC's competitors in the enterprise modeling field were other small companies. That changed, starting in about 2000, when VSC's small competitors were acquired by large companies such as IBM, Microsoft, CA, and Telelogic. Through the use by the large companies of the name and marks of the small acquired companies, the identities and distinctness of the acquired former competitors merged into that of the larger acquirers. Substantially all of the modeling tool names from the 1990s used by VSC's competitors were acquired and rebranded, or disappeared altogether.
Thus, when Unisys started using a mark (3D VISIBLE ENTERPRISE) substantially similar to VSC's VISIBLE mark, that use posed the risk that potential customers of VSC would assume VSC had likewise been acquired by Unisys. This problem was exacerbated because both companies had extensive websites. A customer searching for "Visible" and "enterprise modeling" could be led to Unisys. Given Unisys' large online presence, the use of the term "Visible" by the junior user, Unisys, threatened to overwhelm the mark of the senior user, VSC. The risk was that VSC would be thought to have *73 disappeared into Unisys, to the detriment of VSC's sales. The question is whether a rational jury could conclude that there was a likelihood of this sort of reverse confusion.
Our caselaw has long had a non-exclusive list of factors against which a finding of a likelihood of confusion is assessed. See Beacon Mut. Ins. Co. v. OneBeacon Ins. Group, 376 F.3d 8, 15 (1st Cir.2004). In Attrezzi we described one such representative list, and applied the analysis to a reverse confusion case:
In assessing confusion, this circuit has resorted to the consultation of a series of factors ... [that] includes: (1) the similarity of the marks; (2) the similarity of the goods (or, in a service mark case, the services); (3) the relationship between the parties' channels of trade; (4) the juxtaposition of their advertising; (5) the classes of prospective purchasers; (6) the evidence of actual confusion; (7) the defendant's intent in adopting its allegedly infringing mark; and (8) the strength of the plaintiff's mark.
Attrezzi, 436 F.3d at 39 (quoting Int'l Ass'n of Machinists v. Winship Green Nursing Ctr., 103 F.3d 196, 201 (1st Cir. 1996)); see also Venture Tape Corp. v. McGills Glass Warehouse, 540 F.3d 56, 60-61 (1st Cir.2008). The district court expressly incorporated these factors[3] into its instructions to the jury. It cautioned the jury not to consider any one factor as conclusive.
Using such a list as a check against jury irrationality, the application of these factors to the facts of record in this case rationally support a finding of likelihood of reverse confusion. The jury found the parties' marks were "substantially similar." Unisys argues they were not so similar as to support a likelihood of reverse confusion. Both Unisys and VSC use the word "Visible," even though Unisys used the word primarily as part of the phrase "3D Visible Enterprise." Unisys argues that the two marks have different typefaces, backgrounds, and visual cues. Even so, the dissimilarities are not so great as to render irrational the finding of likelihood of reverse confusion.
Unisys argues that the two companies have dissimilar offerings and "are in fundamentally different businesses." While VSC primarily sells goods, in the form of software, Unisys sells services, in the form of consulting. A rational finding of reverse confusion, was possible, even so. Dr. Malcolm Lane, an expert witness for the plaintiff, testified that Unisys' and VSC's offerings were "very similar and have very similar outputs and results for clients." A jury could conclude that in the field of enterprise modeling through computer applications, there was a realistic likelihood of reverse confusion. This is not a case in which the two companies' offerings are so dissimilar as to make confusion highly unlikely. See Attrezzi, 436 F.3d at 39.
Similarities between channels of trade, advertising, and prospective customers are related factors, are often considered together, see id. at 39-40, and support the jury verdict. Unisys argues that the two companies differ greatly: (1) while VSC's product sales occur primarily through downloads from its website, Unisys' consulting engagements result from longstanding client relationships; (2) VSC primarily markets through its website, while *74 Unisys advertises in general business publications, though both companies market extensively on the internet. Still, the jury heard testimony that both parties targeted many of the same customers. In addition, there was evidence of overlap between the parties' channels of trade. For example, the jury heard testimony that VSC's clients, such as the Arizona court system, signed ongoing consulting contracts of the kind Unisys identifies as its own primary channel of trade.
While VSC presented no evidence of actual confusion at trial, the jury could have inferred actual reverse confusion from the company's decline in revenues from the sales of its software products. And actual confusion is not a prerequisite to a finding of likelihood of confusion. See Borinquen Biscuit Corp., 443 F.3d at 120-21.
In a reverse confusion case, the focus is on the relative strengths of the marks so as to gauge the ability of the junior user's mark to overcome the senior user's mark.[4]See 4 McCarthy, supra, § 23:10, at 23-54 to -55 (citing Checkpoint Sys., Inc. v. Check Point Software Techs., Inc., 269 F.3d 270, 303 (3d Cir.2001)). A jury could conclude the Unisys mark could overcome the VSC mark. Unisys had a national advertising campaign for 3D Visible Enterprise, promoted the 3D Visible Enterprise campaign on the internet, and built the 3D VISIBLE ENTERPRISE mark through partnerships with developers of modeling tools. The VISIBLE mark had been used by VSC for over twenty years, VSC had spent over $2 million to promote the mark since 1987, and VSC had acted in the past to protect its mark. A jury could reasonably find that these facts established the identity of VSC's mark, but did not prevent the mark from being overwhelmed by Unisys' mark.
In sum, the jury could rationally have found a likelihood of reverse confusion.

B. Sufficiency of Evidence To Support Jury Award of $250,000 in Damages

Unisys argues that the evidence is insufficient to support the damages award, a challenge we review de novo to determine whether "reasonable persons could not have reached the conclusion that the jury embraced." Attrezzi, 436 F.3d at 37 (quoting Sanchez v. P.R. Oil Co., 37 F.3d 712, 716 (1st Cir.1994)). The test for Unisys "is a stringent one," requiring Unisys to demonstrate a "total failure of evidence to prove plaintiff's case." Id. (quoting Vázquez-Valentín v. Santiago-Díaz, 385 F.3d 23, 29 (1st Cir.2004), vacated on other grounds, 546 U.S. 1163, 126 S.Ct. 1329, 164 L.Ed.2d 43 (2006)) (internal quotation marks omitted).
Unisys argues that there was no proof of either actual harm or of causation, pointing to evidence that VSC's revenues had been in decline before Unisys' launch in 2004 of the 3D Visible Enterprise campaign. It argues that the decline in VSC's revenues immediately following the June 2004 publication of Unisys' advertisement in the Wall Street Journal represented one of a normal series of fluctuations in VSC's revenues and was not caused by the launch of Unisys' campaign.[5]
*75 Nonetheless, the jury heard testimony that VSC's revenues in the quarter immediately following the launch of Unisys' campaign were "[p]robably the lowest in the history of the company." VSC introduced into evidence a chart of its quarterly revenues before and after the infringement as well as its financial statements from the relevant years. The jury could conclude that Unisys' infringement reduced VSC's average monthly revenue by approximately $28,000 in the period immediately following the infringement. Michael Cesino, VSC's President, testified that a later increase in revenues was due to VSC's re-hiring of an experienced salesman. The jury could have reasonably inferred that VSC's revenues would have been higher but for the infringement.
Cesino's testimony provided a basis for the $250,000 figure. He testified the jury could determine VSC's lost profits by calculating a profit margin on operations (using VSC's revenues and operating expenses) and applying that margin to VSC's lost revenues. By using this method, the jury had a basis for determining that an award of approximately $250,000 was appropriate. In fact, VSC argued to the jury that an award of about $500,000 was appropriate. The award was neither excessive nor inadequate, itself a sign that the jury did not behave unreasonably. See Attrezzi, 436 F.3d at 40.

III.

VSC'S APPEAL FROM THE COURT'S EXCLUSION OF EVIDENCE OF BAD FAITH, THE REFUSAL TO ISSUE A BROADER INJUNCTION, THE DENIAL OF AN ACCOUNTING REMEDY, AND THE DENIAL OF ATTORNEYS' FEES

A. Bad Faith

VSC argues that the evidence showed Unisys proceeded in bad faith and that the court erred in deciding otherwise. It uses that argument to buttress its other arguments that it was entitled to other remedies and to attorneys' fees. Because we find no error in the district court's rulings, we have no need to discuss the relevance of bad faith to the other issues in the case. See generally D. Conway-Jones, Remedying Trademark Infringement: The Role of Bad Faith in Awarding an Accounting of Defendant's Profits, 42 Santa Clara L.Rev. 863, 865 (2002) (proposing that "Congress did not intend a bad faith requirement be met before an owner of an infringed mark is able to recover a defendant's profits collected on the back of the infringed mark").
Bad faith, in trademark law, "refers to an attempt by a junior user to exploit the good will and reputation of a senior user with the intent to sow confusion." 4 McCarthy, supra, § 23:113, at 23-357 (quoting Star Indus., Inc. v. Bacardi & Co., 412 F.3d 373, 388 (2d Cir.2005)). Bad faith differs from "willfulness," which arises when an infringer proceeds despite knowledge of the senior user's trademark. See id. § 23:113; see also Tamko Roofing Prods., Inc. v. Ideal Roofing Co., 282 F.3d 23, 31 (1st Cir.2002). The court said it would allow a jury question on willfulness because the jury's answer might be of use in evaluating a later request for attorneys' fees.
VSC's argument about bad faith consists of two inferences it draws from evidence admitted and a subsidiary argument that the court improperly excluded evidence. Bad faith could be inferred, VSC argues, from the alleged failure of Unisys' good faith explanation for how the company developed the 3D VISIBLE ENTERPRISE mark. VSC also argues that evidence that numerous Unisys employees *76 had requested information on VSC's products and had downloaded software from VSC's website supported the inference Unisys knew of and deliberately intended to benefit from VSC's reputation.
The court correctly ruled at summary judgment that the proffered evidence did not show bad faith. For example, the evidence does not provide a basis for the conclusion that Unisys chose the mark 3D VISIBLE ENTERPRISE in order to take advantage of VSC's reputation and goodwill in the market. See Aktiebolaget Electrolux v. Armatron Int'l, Inc., 999 F.2d 1, 6 (1st Cir.1993). Unisys' witness John Aaker, a vice president of the Grey Worldwide advertising agency, testified that it was the advertising agency, not Unisys, which conceived of the 3D VISIBLE ENTERPRISE mark and developed it. Grey, in turn, then caused its counsel to conduct a search for other marks, received advice that Unisys was in a strong position, and went ahead to present the mark to Unisys. The letter from Grey's trademark counsel was admitted into evidence by agreement.
In rebuttal, VSC offered evidence that Unisys had used the terms "3D" and "visible," during an internal marketing event in June 2003 launching its "Business Blueprinting" campaign (a predecessor of the 3D Visible Enterprise campaign) and that the advertising agency had reviewed a video of the event. This evidence is insufficient for a conclusion that Unisys "tried a scheme to launder its 3D VISIBLE ENTERPRISE mark" through the advertising agency.
Evidence was admitted of a list of Unisys employees who had since 1988 requested information from VSC or downloaded information from its website. The evidence showed that some Unisys marketing employees and other employees were aware of VSC's mark in 1996, almost a decade earlier, but VSC did not call witnesses or connect any of the listed employees to the 2004 adoption of the 3D VISIBLE ENTERPRISE mark. That is not enough to show bad faith. See Century 21 Real Estate Corp. v. Century 21 Real Estate, Inc., 929 F.2d 827, 829 (1st Cir. 1991). This is particularly true given the different slants in the two businesses  one slanted to sales of software, the other to sales of consulting services.
VSC also proffered additional evidence on bad faith, consisting of Unisys' post-suit internal communications, such as prohibitions on use of the term "visible" in product or service marks with the exception of the 3D VISIBLE ENTERPRISE mark, that VSC argued showed willfulness in Unisys' later deployment of additional marks that contained the term. The district court did not abuse its discretion in excluding this evidence.

B. VSC's Request for Broader Injunctive Relief

Our review of the trial court's choice of injunctive relief is for abuse of discretion. Metro-Goldwyn Mayer, Inc. v. 007 Safety Prods., Inc., 183 F.3d 10, 14-15 (1st Cir. 1999). The terms of the injunction issued enjoined Unisys "from using the trademarks or service marks 3D VISIBLE ENTERPRISE, 3D-VE, or VISIBLE, in the sale, offering for sale, distribution or advertising in the United States of goods or services in the enterprise modeling or enterprise architecture fields." The injunction also ordered Unisys to "remove all uses of the 3D VISIBLE ENTERPRISE, 3D-VE, and VISIBLE marks from the Internet website www.unisys.com, and ... [to] remove and destroy all other advertising or promotional materials that are within the United States and within the control of Unisys and that incorporate the marks 3D VISIBLE ENTERPRISE, 3D-VE, and VISIBLE." The injunction allowed *77 Unisys to continue using the marks internally and to continue using "visible" in its ordinary descriptive sense.
VSC argues that the court erred in refusing to bar Unisys' use of VISIBLE on Unisys' country-specific websites based outside of the United States and in allowing Unisys to use "visible" in its ordinary descriptive sense.
VSC argues that allowing Unisys to use VISIBLE in its non-U.S. websites contravenes the principle that Lanham Act jurisdiction may extend to extraterritorial conduct by American citizens that has a substantial effect on domestic commerce. See generally McBee v. Delica Co., Ltd., 417 F.3d 107, 116-18 (1st Cir.2005) (noting that the Lanham Act may reach such conduct but that "[t]he reach of the Lanham Act depends on context"). There was no evidence that VSC maintained any overseas websites or that it had any substantial overseas sales. Its argument to the district court focused on the possibility that domestic customers could access Unisys' overseas websites from the United States. There was no error of law or abuse of discretion; the court's stated reason for rejecting VSC's broader language was that it found the proposed injunction "simply so broad ... as [to be] largely unworkable in the real world."
VSC's challenge to allowing Unisys to use the word "visible" in its ordinary descriptive sense also fails. VSC argues the court's decision was error because the trial record disclosed no use in the relevant field of "visible" as a descriptive term. The trial court had "first-hand exposure to the litigants and the evidence," Rosario-Torres v. Hernandez-Colon, 889 F.2d 314, 323 (1st Cir.1989) (en banc), and it acted well within its discretion[6] in deciding that a narrower prohibition would be adequate to prevent future harm.

C. VSC's Claim to an Accounting of Unisys' Profits and for a Jury Trial on That Issue

There is no dispute that VSC was entitled to and received a jury trial for VSC's claim of its own damages for infringement, though the request was joined with a request for equitable relief. See Beacon Theatres, Inc. v. Westover, 359 U.S. 500, 508-11, 79 S.Ct. 948, 3 L.Ed.2d 988 (1959); Attrezzi, 436 F.3d at 36.
VSC argues that it was also entitled under both the Act and the Seventh Amendment to a jury trial, under Dairy Queen, Inc. v. Wood, 369 U.S. 469, 82 S.Ct. 894, 8 L.Ed.2d 44 (1962), on its request for an accounting of defendant's profits. It had earlier sought $100 million for an accounting from the court, which was denied. The question of what role a jury plays as to the remedy of an accounting in a Lanham Act case is complicated.
VSC argues the Lanham Act gives it a statutory right to a jury trial on the remedy of an accounting. The Lanham Act directs that the question of entitlement of plaintiffs to defendants' profits be subject to "the principles of equity":
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 in any civil action arising under this chapter, the plaintiff shall be entitled, ... subject to the principles of equity, to recover (1) defendant's profits,

*78 (2) any damages sustained by the plaintiff, and (3) the costs of the action.
15 U.S.C. § 1117(a). The remedial provisions of the Lanham Act authorize four forms of relief: an accounting of the defendant's profits, any damages sustained by the plaintiff, the costs of the action, id., and injunctive relief under § 1116(a). However, even the monetary relief available under § 1117(a) is "subject to the principles of equity." Further, "if the court ... find[s] that the amount of the recovery based on [defendant's] profits is either inadequate or excessive the court may in its discretion enter judgment for such sum as the court shall find to be just, according to the circumstances of the case."[7]Id. The Lanham Act prohibits the use of such relief as a penalty. Under the Act's language, even if a jury were to determine the amount of defendant's profits, a court could in its discretion set the jury award aside if the profits were excessive.[8] Plaintiff has argued only that there is an initial right to a jury trial, not that the court lacks power to set aside an award under the terms set in the Act.
VSC concedes that an accounting is generally described as an equitable remedy, see 15 U.S.C. § 1117(a); see also Tamko, 282 F.3d at 36, but correctly says that is not dispositive of the Seventh Amendment question. This court has not directly addressed the question. We have said generally, in a trademark case not raising this precise question, that common-law claims are to be tried to a jury while equitable claims can be tried to a judge. See Attrezzi, 436 F.3d at 36.
In order to avoid reaching the Seventh Amendment question, we ask first if the Lanham Act itself provides for a jury trial, as VSC contends. Under the reasoning of the Supreme Court's opinion in Feltner v. Columbia Pictures Television, Inc., 523 U.S. 340, 118 S.Ct. 1279, 140 L.Ed.2d 438 (1998), construing similar phraseology in the Copyright Act, it seems clear that the Lanham Act itself does not create a right to a jury trial whenever the remedy of an accounting of defendant's profits is sought.
The Seventh Amendment analysis requires a determination of "whether the statutory cause of action is more analogous to cases tried in courts of law than to suits tried in courts of equity or admiralty," which in turn requires examination of "both the nature of the statutory action and the remedy sought." Feltner, 523 U.S. at 348, 118 S.Ct. 1279; see also Markman v. Westview Instruments Inc., 517 U.S. 370, 376, 116 S.Ct. 1384, 134 L.Ed.2d 577 (1996); Granfinanciera, S.A. v. Nordberg, 492 U.S. 33, 41-42, 109 S.Ct. 2782, 106 L.Ed.2d 26 (1989).
VSC's opening brief provides no argument at all on this required examination but does cite to commentary in a respected treatise. See 6 McCarthy, supra, § 32:124, at 32-261 ("[A] claim for an accounting of defendant's profits is usually treated for jury trial purposes as the equivalent of a claim for legal damages."). Its reply brief offers little more.
No federal court of appeals decision which extensively discusses the issue has been called to our attention by the parties. *79 One law review article on the topic concludes that the issue of an accounting of defendant's profits in a trademark action is for the court, based on its review of the history of the remedy. M. Thurmon, Ending the Seventh Amendment Confusion: A Critical Analysis of the Right to a Jury Trial in Trademark Cases, 11 Tex. Intell. Prop. L.J. 1, 6 (2002).
The power of a trial judge to determine that the evidence is insufficient to support an award of a disgorgement of the infringers profits is unaffected by the Dairy Queen rule. To the extent VSC is arguing that the district court is precluded from making this assessment of the evidence either at summary judgment or after trial, we reject the argument. The court is, at the least, the initial gatekeeper as to whether the evidence suffices. See Quick Techs. Inc. v. Sage Group PLC, 313 F.3d 338, 349 (5th Cir.2002). The Supreme Court established at least this much in Champion Spark Plug Co. v. Sanders, 331 U.S. 125, 67 S.Ct. 1136, 91 L.Ed. 1386 (1947).[9] In Champion Spark Plug, the Supreme Court held that courts must take equitable principles into account in determining whether to award an accounting of profits. 331 U.S. at 131, 67 S.Ct. 1136. There, the court upheld the decision of both the trial and appellate courts to deny an accounting and held the remedy is not automatic as a result of an infringement finding. Id. at 131-32, 67 S.Ct. 1136.
Here, the court ruled that the issue of an accounting is for the court, not a jury.[10] The trial judge also ruled that the evidence to support the remedy of an accounting was insufficient to reach the jury, stating that if the jury made such an award, the court would be forced "to throw it out." If the evidence was insufficient to justify an accounting (as we hold), then the question of whether there is a Seventh Amendment jury trial right to an accounting becomes academic and can be avoided.
Our review of the sufficiency question is de novo. Attrezzi, 436 F.3d at 37. This circuit, like others, has recognized three rationales for awarding to the plaintiff an accounting of the defendant's profits: "(1) as a rough measure of the harm to plaintiff; (2) to avoid unjust enrichment of the defendant; or (3) if necessary to protect the plaintiff by deterring a willful infringer from further infringement." Tamko, 282 F.3d at 36. The sufficiency of the evidence must be evaluated against each of the rationales for an award of the defendant's profits. On this record, we agree with the trial judge's assessment, under any of the standards of review, that none of those rationales would be served by an accounting.
*80 The first rationale for an accounting is as a proxy for legal damages, that is, a rough measure of harm to the plaintiff.[11]Dairy Queen itself held that "[t]he necessary prerequisite to the right to maintain a suit for an equitable accounting ... [is] the absence of an adequate remedy at law." 369 U.S. at 478, 82 S.Ct. 894. The proxy rationale has no place in this case on the evidence.
The harm to plaintiff was in fact measured and damages were awarded. The jury answered a special question, "[p]lease state, in words and figures, the dollar amount of damages which you have determined defendant Unisys Corporation should pay to plaintiff Visible Systems Corporation in order to restore it to the position it would have been in had the infringement not occurred" (emphasis added), and awarded $250,000 to VSC, as recompense for the harm VSC suffered.
Furthermore, the district court concluded[12] that the evidence did not show there were profits which accrued to Unisys as a result of its infringement. Our prior discussion of the evidence[13] supports the district court's conclusion. Indeed, at trial VSC "[did] not contend that potential customers of Unisys are likely to make purchasing decisions about its goods and services under the mistaken belief they are associated with Visible Systems."
Rather, plaintiff's theory of harm was one of reverse confusion, and reverse confusion does not lend itself to any automatic assumption that there is an equivalence between defendant's profits and plaintiff's diverted sales. See Johnny Blastoff, Inc. v. L.A. Rams Football Co., 188 F.3d 427, 436-37 (7th Cir.1999) (noting that in reverse confusion cases, the infringer does not seek to profit from the senior user's goodwill but nevertheless causes indirect harm to the senior user); Big O Tire *81 Dealers, Inc. v. Goodyear Tire & Rubber Co., 561 F.2d 1365, 1374 (10th Cir.1977); Restatement (Third) of Unfair Competition § 37 cmt. b (1995) ("The correspondence is clearly imperfect, however, since in most cases there is no reason to expect that every sale made by the defendant has been diverted from the plaintiff, or that the profit margins of the parties are necessarily the same."). This case is not a suitable candidate for the proxy rationale for an accounting.
VSC relies primarily on the second rationale for an accounting  avoidance of unjust enrichment of the infringing defendant. We assume that it is possible both for one party to have suffered lost profits from its own declining sales and for the infringer to have been unjustly enriched by its infringement. Still, as we have said, the evidence is that Unisys made no unjust profits and so was not unjustly enriched.
The third rationale, that an accounting can be justified if necessary to protect the plaintiff by deterring a willful infringer from further infringement, also has no place here based on the evidence. That rationale requires, at a minimum, that the defendant has acted willfully, as the jury did find here. See Tamko, 282 F.3d at 36 n. 11. Still, willfulness alone is not enough to justify a remedy of an accounting of defendant's profits where there is a damages award to the plaintiff, no showing of unjust enrichment, no bad faith, and an injunction has been entered.
The fact that injunctive relief has been entered does not alone preclude an accounting, Tamko, 282 F.3d at 35, but it is highly pertinent to the adequacy and completeness of the remedy. The injunction here provides adequate deterrence. It prevents Unisys from using the VISIBLE, 3D VISIBLE ENTERPRISE, or 3D-VE marks in the enterprise modeling and architecture fields. The injunction also provides for a dispute resolution procedure in the event VSC believes Unisys has violated its terms. The presence of the injunctive relief also promotes the goal of increasing confidence in the market economy. Cf. Conway-Jones, supra, at 882.

D. Denial of Attorneys' Fees

The Lanham Act provides for attorneys' fees only "in exceptional cases." 15 U.S.C. § 1117(a). VSC challenges the court's order declining to award fees, arguing that the factors identified in Tamko for deciding whether to award fees weigh in its favor. Congress left it to the court, not the jury, to consider whether an award of attorneys' fees is equitable. Tamko, 282 F.3d at 31 n. 5.
We review the legal question of the meaning of "exceptional cases" de novo and the district court's denial of an award of attorneys' fees for abuse of discretion. To the extent that the district court's award rests on factual determinations, however, we review those for clear error. Id. at 30.
There is no "per se equivalence between `exceptional case' and a jury finding of willfulness." Id. at 31 n. 5. Among the factors we have identified in guiding a court's decision on an award of fees are whether:
[T]he area of law is unclear and defendants might reasonably think they did not infringe; there is a close legal question as to whether there is any trademark violation; defendant had no intent to deceive or confuse the public; the defendant made a concerted effort to create a non-infringing mark; the plaintiff suffered no actual damage.
*82 Id. at 32-33 (citations omitted). The district court reviewed these factors and committed no error of law.
The court did not abuse its discretion in concluding that "little, if anything, about this case could be appropriately deemed exceptional or extraordinary." It reasoned that Unisys had a good faith belief that it was not in competition with VSC, that the evidence that VSC suffered actual damage was indirect, and that Unisys' behavior did not rise to the level of deliberate and willful conduct as was the case in Tamko. Indeed, at the summary judgment stage, the district court characterized the plaintiff's case as "thin," a relevant consideration. See Raxton Corp. v. Anania Assocs., Inc., 668 F.2d 622, 625 (1st Cir.1982).

IV.
We affirm the judgment of the district court. Each side shall bear its own costs.
NOTES
[1]  No claim is made in this case of dilution in violation of the Federal Trademark Dilution Act, codified at 15 U.S.C. § 1125(c), or of cybersquatting under the Anticybersquatting Consumer Protection Act, codified at 15 U.S.C. § 1125(d)(1)(B)(i)(I)-(IX).
[2]  VSC did not advance an argument that Unisys offered inferior products, an alternate theory of harm from reverse confusion. Attrezzi, 436 F.3d at 39.
[3]  The court did not instruct the jury on the question of the defendant's intent as a separate factor but rather, instructed the jury to consider Unisys' intent in deciding whether Unisys acted willfully, an issue the jury was to address only if it found infringement. There was no objection.
[4]  Both VSC's and Unisys' proposed instructions, as well as the court's ultimate instructions to the jury, focused on the strength of VSC's mark rather than the strength of Unisys' mark. Neither party raised an objection to the court's instructions.
[5]  We do not need to discuss in detail Unisys' argument that VSC waived any claim to damages based on harm to its goodwill. VSC's counsel argued for an instruction on damages based on harm to the company's goodwill and the district court itself later stated that the colloquy did not constitute a waiver.
[6]  Unisys argues that because VSC was not entitled to any injunctive relief at all due to unclean hands, it cannot complain about the limits on the injunctive relief it did get. There is no need to address the argument.
[7]  As McCarthy notes, the remedy of an accounting of profits has its historic roots in equity jurisprudence. "An accounting of profits is never automatic. The courts retain the right to withhold the remedy if, in view of the overall facts and equities of the case, it is not appropriate." 5 McCarthy, supra, § 30:59, at 30-138 to -139 (footnote omitted).
[8]  Of course, even if the accounting is viewed as an equitable claim for the judge, the judge is bound by the jury's determination of issues, such as the jury's finding of willfulness, which affect the disposition of the accompanying equitable claim. Attrezzi, 436 F.3d at 43 n. 5.
[9]  Whether the precise holding of Champion Spark Plug survives the various amendments to the Lanham Act in 1999 is not an issue we need to address. See B. Banner, Trademark Infringement Remedies 7-3 (2006). We note McCarthy's view that the purpose of the 1999 Amendment of Lanham Act § 35(a) was to be clear that in dilution cases, and only dilution cases, Congress meant to limit this recovery to instances of willful violation. 5 McCarthy, supra, § 30:62, at 30-145.
[10]  Whether there is a jury trial right on the issue of an accounting of the infringer's profit could affect the standard of appellate review. If the issue were committed to the discretion of the court, either because there is no jury trial right or because the court under the statute may adjust a jury award in light of equitable considerations, we would review the court's ultimate finding for abuse of discretion. See Venture Tape, 540 F.3d at 62; see also Hoult v. Hoult, 373 F.3d 47, 53 (1st Cir.2004) (describing abuse of discretion standard). If, however, the issue of an accounting of damages was ordinarily for the jury, at least in the first instance, then appellate review would be for whether the evidence was sufficient to put the issue to the jury.
[11]  In our view, this proxy rationale may well present the strongest argument under the Seventh Amendment; we do not decide the point. This does not mean that a plaintiff's characterization of why it is seeking an accounting would control, even under our hypothetical. See Thurmon, supra, at 90-91, 101 (noting that focusing on the proxy rationale may invite manipulation of the jury trial guarantee through artful pleading); id. at 107 (noting that courts of equity historically awarded an accounting of defendant's profits as a substitute for a damages claim at law); see also Juicy Couture, Inc. v. L'Oreal USA, Inc., No. 04 Civ. 7203, 2006 WL 559675, at *1-2 (S.D.N.Y. Mar.7, 2006) (refuting a plaintiff's strategic attempt to assert a proxy rationale).
[12]  The court denied summary judgment on this issue but reconsidered the issue at trial after VSC brought new facts to its attention and then decided in the chambers charge conference that the evidence was insufficient to support an accounting. We do not have the benefit of a full statement of the district court's reasoning. We reject VSC's criticism of the district court for not conjuring up some memory of what was said when there was no documentation. VSC easily could have asked for a reporter to be present at the charge conference.
[13]  To recap, VSC primarily sold software, which constituted approximately 80 to 90% of its revenues, and its consulting sales in fact increased during the period of Unisys' infringement. By contrast to VSC's sale of software, Unisys never sold its own software. Unisys sold consulting services; when, in those instances of providing consultant services, the client also wanted software, Unisys consultants were "tool agnostic" and provided third-party products. While VSC and Unisys targeted similar customers, VSC's consulting clients primarily sought support in using VSC's software products; Unisys' consulting clients primarily sought business advice without regard to which software was used. VSC's consulting engagements were largely limited to training and mentoring VSC's clients in using VSC's products. Further, VSC eliminated the position of Vice President of Client Services and employed no full-time consultants at the time of the infringement.
