POSNER, Circuit Judge.

This litigation, now in its fourth year, is between competing manufacturers of highspeed turbo blowers used by waste water treatment plants. The blowers maintain the oxygen dissolved in the water at a level needed by the aerobic (that is, oxygen-dependent) bacteria that play a critical role in the treatment process by breaking down organic waste into carbon dioxide, nitrogen, and water. The plaintiffs operate in the United States as a joint venture under the name APG-Neuros, and to simplify exposition we'll pretend that APG-Neuros is the plaintiff and (for further simplification) call it Neuros.

Neuros was the first company to offer such blowers to waste water treatment facilities in North America. That was in 2006 and two years later the Defendant KTurbo, began offering its own blowers to those facilities, though with little success.

In 2008 Neuros won a bidding contest to supply high-speed turbo blowers to a waste water treatment plant in Utah. KTurbo came in third in the bidding — last, because there were only three bidders. Disappointed with the outcome of the bidding contest, the chief executive officer of KTurbo, HeonSeok Lee, prepared a series of PowerPoint slides and related tables that accused Neuros of fraud by representing to the Utah purchaser that its blowers would achieve a "total efficiency" that Lee claimed, probably correctly, was unattainable.

Waste water treatment plants hire consulting engineers to select, test, and install the turbo blowers. Lee's slides were aimed at those engineers. Here is a typical slide:

Turbo blowers are fans driven by electricity, and they use a lot of it — and it's expensive; the cost of electricity is the second largest cost (after labor) of operating a waste water treatment plant, and the blowers account for a substantial fraction of the electricity cost. M/J Industrial Solutions, "Municipal Wastewater Treatment Plant Energy Baseline Study," PG & E New Construction Energy Management Program, pp. 5-6 (June 2003), www.cee1. org/ind/mot-sys/ww/pge1.pdf (visited Oct. 9, 2012). "Total efficiency," the key term in Lee's slides, is the ratio of input power (electrical current) to output power (a specified volume of air blown by the blower at a specified speed). Were there no power loss, making the ratio 1, total efficiency would be 100 percent. Even 82.5 percent of total efficiency, the figure that the slide accused Neuros of claiming to have attained, appears to be unattainable. But Neuros did not make representations of total efficiency. It made representations of "wire power," which is the ratio of an electrical current to work (such as turning the blades of a fan); and to estimate total efficiency from wire power requires consideration of other factors as well, such as temperature and humidity.

KTurbo's PowerPoint presentation states that some of Neuros's claims of wire power imply that its efficiency claims are exaggerated, but these accusations turned out to be false too. They were based on computational errors and incorrect assumptions. KTurbo's expert argued that the wire power claimed in one Neuros document implied a 2 to 7 percent overstatement of the efficiency of its blowers, but such overstatements do not, as KTurbo argues, make its defamatory accusations "substantially truthful." For KTurbo claimed that the overstatement was not 2 to 7 percent but at least 15-20 or even 26 percent. There was no evidence of such overstatement; KTurbo's expert would not support it.

It was from Neuros's claims of wire power that KTurbo deduced that Neuros was implicitly claiming a total efficiency of 82.5 percent. Lee admits that the wire power claims imply at most a total efficiency of 76 percent, apparently an attainable percentage.

Had KTurbo merely accused Neuros of "guaranteeing" unattainable performance, in the sense of warranting it, this would not necessarily have been an accusation of fraud. One can warrant a level of performance that one may not be confident of attaining, for by accepting a warranty a customer grants the seller an option to pay rather than perform. Cf. Zapata Hermanos Sucesores, S.A. v. Hearthside Baking Co., 313 F.3d 385, 389 (7th Cir.2002); Oliver Wendell Holmes, Jr., The Common Law 300-02 (1881). The slide we reproduced earlier did describe the alleged representation that Neuros's blowers achieve 82.5 percent of total efficiency as a "guarantee." But Neuros had never warranted that performance, and so if it had represented that its blowers were that efficient, knowing they were not, the representation would have been fraudulent; and that is what KTurbo claimed.

Lee made his PowerPoint presentation to a number of the engineering firms that advise waste water treatment plants on which turbo blowers to buy. Judging from the fact that KTurbo failed, so far as appears, to wrest any business from Neuros, the consulting engineers were not impressed by the slide show. Lee also published his accusations on one of KTurbo's websites and sent them to the sales representatives that the company uses to help market its blowers, doubtless hoping the representatives would convey the accusations to the engineers whom they visited on KTurbo's behalf. KTurbo vowed in correspondence to "break" and "terminate" Neuros. All to no avail. KTurbo was like a gnat that buzzes annoyingly around a person's head but never manages to land and bite.

The suit charges KTurbo with violations of the Lanham Act and the Illinois Uniform Deceptive Trade Practices Act, and with defamation, also under Illinois law. KTurbo filed parallel counterclaims. A bench trial resulted in a judgment in favor of Neuros on its claim of defamation and an award of $10,000 in general damages and $50,000 in punitive damages. The judge rejected all other claims, including the counterclaims. KTurbo's appeal challenges only the judgment for defamation; Neuros's cross-appeal challenges the dismissal of its Lanham Act and Deceptive Trade Practices Act claims.

KTurbo argues that even if it defamed Neuros by false statements (as clearly it did), it had a "qualified privilege" to do so. This privilege is available in cases in which the public had an "interest" in the making of the statements that turned out to be false. Kuwik v. Starmark Star Marketing & Administration, Inc., 156 Ill.2d 16, 188 Ill.Dec. 765, 619 N.E.2d 129, 134-35 (1993); Parker v. House O'Lite Corp., 324 Ill.App.3d 1014, 258 Ill.Dec. 304, 756 N.E.2d 286, 298 (2001); Haywood v. Lucent Technologies, Inc., 323 F.3d 524, 533 (7th Cir.2003) (Illinois law); Restatement (Second) of Torts §§ 593-98A, 598 comments d-f (1977). This is pretty vague, but we needn't worry about that in this case, since the privilege, whatever its precise boundaries, is forfeited if the statement is made with knowledge of its falsity or with reckless disregard for the truth (which courts in defamation cases like to call "actual malice" — why we don't know, since "malice" implies deliberate rather than merely reckless wrongdoing). Kuwik v. Starmark Star Marketing & Administration, Inc., supra, 188 Ill.Dec. 765, 619 N.E.2d at 135-36; Naleway v. Agnich, 386 Ill.App.3d 635, 325 Ill.Dec. 363, 897 N.E.2d 902, 913 (2008); Giant Screen Sports v. Canadian Imperial Bank of Commerce, 553 F.3d 527, 536 (7th Cir.2009) (Illinois law); Restatement, supra, § 600. KTurbo was warned repeatedly, not only by Neuros but also by disinterested sources, that its accusations were false; it ignored the warnings and refused to investigate the truth of the accusations. Its conduct was not only disreputable but reprehensible.

KTurbo complains perfunctorily about the award of punitive damages. The general rule is no injury no tort, McCann v. Hy-Vee, Inc., 663 F.3d 926, 930-31 (7th Cir.2011), and there is no evidence that Neuros was injured by the false claims that KTurbo made. But there are exceptions (which is why we call it the "general" rule). One is for trespass, because a continuing trespass may ripen into a prescriptive right and thus deprive a property owner of title to his land. Another is for defamation per se, which means, so far as relates to a business victim, defamation that impugns the defendant's competence or honesty. Tuite v. Corbitt, 224 Ill.2d 490, 310 Ill.Dec. 303, 866 N.E.2d 114, 121 (2006). And that was the character of KTurbo's defamation of Neuros. KTurbo accused it of committing criminal fraud against its customers. It's hard to imagine a more damaging accusation to make against a business.

When defamation per se is proved, the plaintiff is entitled both to general damages — which means "compensatory" damages without proof of injury, id.; Van Horne v. Muller, 185 Ill.2d 299. 235 Ill.Dec. 715, 705 N.E.2d 898, 903 (1998); Restatement, supra, § 621 comment, a — and, if the defendant in committing the defamation was grossly negligent or worse, to punitive damages as well. Slovinski v. Elliot, 237 Ill.2d 51, 340 Ill.Dec. 210, 927 N.E.2d 1221, 1224-25, 1228-29 (2010). Compensatory damages without proof of injury sounds like an oxymoron, though: for what is there to compensate? But there can never be assurance that an accusation, however groundless, is not believed by someone, and doubtless employees or sales reps of Neuros had to answer questions put to them by consulting engineers, and perhaps even by shareholders of the parent companies, concerning Lee's inflammatory accusations. So a modest award of damages, though not based on evidence (what kind of "evidence" would enable an accurate estimate of the type of cost that we've suggested Neuros incurred from the defamation?), can reasonably be thought compensatory. The judge may have pulled the $10,000 figure out of his hat, but the figure is appropriately modest, considering that a single high-speed turbo blower costs more than $100,000 and that the APG-Neuros joint venture sold some 500 of them in the first few years of its existence.

The punitive damages award of $50,000 was too small, and though Neuros is not seeking more, we cannot forbear to note that the conduct of KTurbo was outrageous and that it is a substantial company. It should have been ordered to pay substantial punitive damages. In ordering the slap-on-the-wrist award that he did the district judge may have been concerned that any multiple of general damages greater than five would run afoul of the Supreme Court's decisions placing tight limitations, in the name of due process, on the ratio of punitive to compensatory damages. In State Farm Mutual Automobile Ins. Co. v. Campbell, 538 U.S. 408, 425, 123 S.Ct. 1513, 155 L.Ed.2d 585 (2003), the Court said that "few awards [of punitive damages] exceeding a single-digit ratio between punitive and compensatory damages, to a significant degree, will satisfy due process.... [F]our times the amount of compensatory damages might be close to the line of constitutional impropriety." But the Court quickly added that there was merely "a presumption against an award that has a 145-to-1 ratio," id. at 426, 123 S.Ct. 1513 (emphasis added) — the award the lower court had upheld — and as we explained in Mathias v. Accor Economy Lodging, Inc., 347 F.3d 672 (7th Cir. 2003), the presumption can be rebutted in cases in which the award of compensatory damages is very small, as indeed the Supreme Court had indicated in the State Farm case, 538 U.S. at 425, 123 S.Ct. 1513; see also BMW of North America, Inc. v. Gore, 517 U.S. 559, 582-83, 116 S.Ct. 1589, 134 L.Ed.2d 809 (1996); Kunz v. DeFelice, 538 F.3d 667, 679 (7th Cir.2008); Alexander v. City of Milwaukee, 474 F.3d 437, 454 (7th Cir.2007). "The proper focus of analysis of the ratio itself is the adequacy of the combined award of compensatory and punitive damages to motivate the prosecution of a meritorious claim. If compensatory damages are slight, a single-digit ratio is likely to be insufficient." Gavin v. AT & T Corp., 464 F.3d 634, 641 (7th Cir.2006).

The gravity of the injury to the victim of a wrongful act is only one consideration in determining a proper penalty, as is obvious if one thinks of punishments, often severe, for criminal attempts that inflict no injury at all. Or if one considers the factors that enter into the determination of fines for crimes committed by firms and other organizations. See, e.g., U.S.S.G. § 8C2.4(a). A principal goal of punishment is deterrence, and in the Mathias case an award of punitive damages capped at $20,000 ($40,000 for the two plaintiffs), as urged by the defendant because that would be four times the compensatory award, would have had a negligible deterrent effect. That may be true of the award of $50,000 in this case, considering the potential gains to KTurbo had it succeeded in expelling its foremost competitor from the North American market. It should consider itself fortunate that Neuros hasn't challenged the adequacy of the punitive-damages award.

So much for defamation; let us turn to Neuros's challenge to the dismissal of its Lanham Act claim. The dismissal may seem academic given the absence of provable injury, for there is no contention that general damages may be awarded for violating the Lanham Act, and the Act limits punitive damages to threefold the actual damages, 15 U.S.C. § 1117(a) — an even lower ratio than the punitive-damages award made by the district judge to punish KTurbo for defamation. But the Act permits the award of attorneys' fees to the prevailing party in "exceptional cases," id., a term the meaning of which we struggled with in Nightingale Home Healthcare, Inc. v. Anodyne Therapy, LLC, 626 F.3d 958 (7th Cir.2010), concluding that an award is appropriate if the opposing party's "claim or defense was objectively unreasonable — was a claim or defense that a rational litigant would pursue only because it would impose disproportionate costs on his opponent." Id. at 965. It is also appropriate when a party's violation of the Act is especially egregious. See, e.g., BASF Corp. v. Old World Trading Co., 41 F.3d 1081, 1099 (7th Cir.1994). The determination of unreasonableness or egregiousness is to be made in the first instance by the district court, which wasn't done in this case because the judge ruled the Lanham Act inapplicable. If that ruling was error, which we have now to consider, the case must be remanded for consideration of whether to award attorneys' fees — plus injunctive relief, authorized in the same section of the Act and also sought by Neuros and denied by the district court.

Without meaning to prejudge the determination on remand, we point out that KTurbo persisted in its false representations to the engineering community concerning Neuros's blowers even after the suit was filed and compelling evidence was presented that the representations were false. This weighs in favor of an award of attorneys' fees by indicating that this part of KTurbo's defense (as opposed to its argument that the Lanham Act was inapplicable because KTurbo was not engaged in advertising or promotion, a respectable argument, as we're about to see) was objectively unreasonable: KTurbo persisted in denying that the slide show and related marketing activities were deceptive long after it was evident that the denial was frivolous.

But is the Lanham Act applicable? It's limited to misrepresentations "in commercial advertising or promotion," 15 U.S.C. § 1125(a)(1)(B), and in Sanderson v. Culligan Int'l Co., 415 F.3d 620, 624 (7th Cir. 2005), we held that three person-to-person communications at trade shows did not constitute commercial advertising or promotion, while in First Health Group Corp. v. BCE Emergis Corp., 269 F.3d 800, 803-04 (7th Cir.2001), we said that the statutory term is limited to "promotional material disseminated to anonymous recipients" and that "an advertisement read by millions (or even thousands in a trade magazine) is advertising, while a person-to-person pitch by an account executive is not," before holding that in any event the defendant's promotional materials did not make false or misleading representations. In between those two decisions came ISI Int'l, Inc. v. Borden Ladner Gervais, LLP, 316 F.3d 731, 733. (7th Cir.2003), which held that sending letters to the plaintiff's business partners, warning them (falsely) that if they continued dealing with the plaintiff they would be liable for patent infringement, was not commercial advertising or promotion.

These cases do not hold that "advertising or promotion" is always limited to published or broadcast materials — an interpretation that would put us at odds with all seven other federal courts of appeals to have considered the issue. LidoChem, Inc. v. Stoller Enterprises, Inc., ___ Fed. Appx. ___, ___, No. 10-1686, 2012 WL 4009709, at *6 (6th Cir. Sept. 12, 2012); Podiatrist Ass'n. Inc. v. La Cruz Azul De Puerto Rico, Inc., 332 F.3d 6, 19-20 (1st Cir.2003); Fashion Boutique of Short Hills, Inc. v. Fendi USA, Inc., 314 F.3d 48, 57-58 (2d Cir.2002); Proctor & Gamble Co. v. Haugen, 222 F.3d 1262, 1273-74 (10th Cir.2000); Porous Media Corp. v. Pall Corp., 173 F.3d 1109, 1121 (8th Cir. 1999); Coastal Abstract Service, Inc. v. First American Title Ins. Co., 173 F.3d 725, 734-35 (9th Cir.1999); Seven-Up Co. v. Coca-Cola Co., 86 F.3d 1379, 1384-85 (5th Cir.1996). All but one of these cases was decided before Sanderson, and four were decided before First Health, and there is no suggestion in either Sanderson or First Health (or for that matter in ISI Int'l) of an intention to create an intercircuit conflict. The cases from the other circuits are not inconsistent with the holding in Sanderson that three person-to-person communications at trade shows do not add up to commercial advertising or promotion or the holding in ISI Int'l that letters threatening suit for patent infringement are not commercial advertising or promotion; and in First Health the Lanham Act was held applicable.

A classic advertising campaign is not the only form of marketing embraced by the statutory term "commercial advertising or promotion." Podiatrist Ass'n required merely "some medium or means through which the defendant disseminated information to a particular class of consumers." 332 F.3d at 20. And the most recent case, LidoChem, explained that "the required level of dissemination to the relevant purchasing public `will vary according to the specifics of the industry.'" ___ Fed.Appx. at ___, 2012 WL 4009709, at *6.

If "advertising or promotion" just meant "advertising," then "promotion" would do no work in the statute. More important (because of the frequency of redundant language in statutes, see, e.g., Lamie v. United States Trustee, 540 U.S. 526, 536, 124 S.Ct. 1023, 157 L.Ed.2d 1024 (2004); Moskal v. United States, 498 U.S. 103, 119-21, 111 S.Ct. 461, 112 L.Ed.2d 449 (1990) (Scalia, J., dissenting); United States v. Costello, 666 F.3d 1040, 1049 (7th Cir.2012); Brown v. Griggsville Community Unit School District No. 4, 12 F.3d 681, 683-84 (7th Cir.1993)), there are industries in which promotion — a systematic communicative endeavor to persuade possible customers to buy the seller's product — takes a form other than publishing or broadcasting. The de facto customers (de facto rather than de jure because they are the purchasers' agents, rather than the purchasers) for high-speed turbo blowers used in waste water treatment plants are the consulting engineers who manage the plants' bidding and purchasing. Lee's road show visited most of the engineering companies that do this, and each show presented promotional materials that trashed Neuros, KTurbo's most prominent competitor.

"Negative" ads — ads that denigrate a competitor — are a conventional though frequently disparaged form of commercial advertising. KTurbo's negative ads reached fewer customers than a conventional campaign, of advertising or promotion would have done, but that was because there are fewer customers for high-speed turbo blowers in waste water treatment plants than there are for dog collars. Road shows are a common method of promotion; it is, for example, the standard method of promoting IPOs. And remember that some of KTurbo's false statements were posted on one of its websites — a reminder that methods of advertising and promotion are changing with innovations in communications media; they are no longer, if they ever were, confined to newspaper and magazine ads, radio and television commercials, and billboards.

The district court was troubled by the fact that "there is no evidence that the statements at issue were presented to any members of the general public." Well of course not; members of the general public do not buy high-speed turbo blowers or advise waste water treatment plants on the purchase of such blowers. There is no basis for limiting the Lanham Act to advertising or promotion directed to the general public, and the case law does not do that. See, e.g., LidoChem, Inc. v. Stoller Enterprises, Inc., supra, ___ Fed.Appx. at ___, 2012 WL 4009709, at *8 (applying the Act to letters sent and statements made to distributors of farm chemicals); Porous Media Corp. v. Pall Corp., supra, 173 F.3d at 1114 (applying the Act to an "alert" sent only to large makers of air filters and to resellers of the filters); Coastal Abstract Service, Inc. v. First American Title Ins. Co., supra, 173 F.3d at 735 (to statements made only to one of two or three national refinancing companies); Seven-Up Co. v. Coca-Cola Co., supra, 86 F.3d at 1381 (only to independent soft drink bottlers). What advertising is not directed to subsets of the public (dog owners in our previous example) rather than to 314 million individuals and millions of firms? One of the subsets is engineering firms, and others are subsets of engineering firms such as the civil engineering firms that were faxed advertisements in CE Design Ltd. v. King Architectural Metals, Inc., 637 F.3d 721 (7th Cir.2011). No one doubted that those advertisements (challenged under a different statute) were — advertising.

The Lanham Act claim should not have been dismissed; nor the parallel claim under the Illinois Uniform Deceptive Trade Practices Act, 815 ILCS 510/1 et seq., a statute generally thought indistinguishable from the Lanham Act except of course in its geographical scope, Muzikowski v. Paramount Pictures Corp., 477 F.3d 899, 907 (7th Cir.2007); Israel Travel Advisory Service, Inc. v. Israel Identity Tours, Inc., 61 F.3d 1250, 1259 (7th Cir.1995); Thompson v. Spring-Green Lawn Care Corp., 126 Ill.App.3d 99, 81 Ill.Dec. 202, 466 N.E.2d 1004, 1013, 1016 (1984), and dismissed by the district court on the same ground as Neuros's claim under the Lanham Act was dismissed.

AFFIRMED IN PART, REVERSED AND REMANDED IN PART.