POSNER, Circuit Judge.

Ty Inc., the manufacturer of "Beanie Babies," years ago brought this suit for trademark infringement under the Lanham Act against Softbelly's, Inc., and some other defendants that need not be discussed separately. Softbelly's manufactures a product that looks and feels very much like "Beanie Babies," which it calls "Screenie Beanies." They differ from Ty's product mainly in having chamois bellies and being sold to the public through computer stores for wiping computer screens: hence the chamois.

The case was tried to a jury back in 2002, but rather than allow it to render a verdict the judge entered judgment for Ty as a matter of law. Later he entered a final judgment awarding Ty both injunctive relief and $713,000 in damages. Softbelly's moved under Fed.R.Civ.P. 60(b)(3) to vacate the judgment in favor of Ty on the ground that Ty Warner, the owner of Ty Inc., had tampered with a prospective witness for Softbelly's. The judge denied the motion.

We reversed. 353 F.3d 528 (7th Cir. 2003). We ruled that Softbelly's was entitled to a new trial on liability because the judge had erroneously excluded potentially important evidence that "Beanies" or "Beanie Babies" had become a generic mark and because he should not have taken the issue of likelihood of confusion from the jury, but that if Ty again prevailed it would be entitled to the $713,000 in damages awarded at the first trial. We also directed the district court to conduct an evidentiary hearing on the charge of witness tampering.

On remand, the case was retried (a different judge presiding). The jury found trademark infringement. The judge entered an injunction forbidding Softbelly's "to sell plush products in connection with the trademarks `Screenie Beanies' and/or `The Screenie Beanies Collection,' and/or any other trademark confusingly similar to Ty's BEANIE BABIES, THE BEANIE BABIES® COLLECTION®, and/or BEANIE (S) TRADEMARKS™." But the judge awarded Ty no damages, holding that forfeiture of the $713,000 in damages to which Ty would otherwise have been entitled by virtue of our ruling in the first appeal was the right sanction for what she found to have been Warner's improper conduct toward the prospective witness. But she awarded Ty the attorneys' fees that it had incurred in proving Softbelly's' trademark infringement, on the ground that the infringement had been willful.

Softbelly's has appealed, seeking yet another new trial on liability and asking that the award of attorneys' fees be vacated. Ty has cross-appealed, seeking vacation of the sanction and thus restoration of the $713,000 in damages that the district judge ordered forfeited. But Ty does not object to our subtracting $78,000 from the restored damages, that being the amount of attorneys' fees that Softbelly's incurred in litigating the issue of Warner's misconduct. Ty had asked for $315,000 in prejudgment interest on the damages award, and so contends that the sanction is really more than $1 million. We need not decide whether, if the sanction should be vacated, Ty is entitled to that interest, an issue that the district judge did not reach and that the parties have not briefed.

The sanctions issue is unconnected to the trademark issues, and as it is the most difficult issue in the case, we address it first. At the first trial, Softbelly's planned to call as one of its witnesses Harold Nizamian, a competitor of Ty for whom Ty Warner had worked before forming his own business. Nizamian was prepared to testify that as early as 1988, before Ty began selling "Beanie Babies," the word "beanie" was being used in the trade names of other manufacturers of plush beanbag animals and indeed that the word had become generic, and so could not be a trademark. On the Friday before the Monday on which the trial began, Softbelly's' lawyer deposed Ty Warner and in the course of the deposition revealed that Nizamian would be testifying that "beanies" was a generic term. On Monday, when the lawyer called Nizamian to schedule his testimony, Nizamian said that Warner had telephoned him and that he was no longer willing to testify.

At the trial, Softbelly's lawyer asked Warner whether he had told Nizamian not to testify. Ty objected and the judge sustained the objection. We ruled that this was error, as was the judge's subsequent action in denying without a hearing Softbelly's' motion to vacate the judgment in favor of Ty on the ground of fraud. In support of the motion Softbelly's had submitted the transcript of a post-trial deposition at which Nizamian had testified that Warner had told him that if he testified at the trial it would cost Warner "a tremendous amount of money" and cause "a lot of problems" since Warner "was involved in the Softbelly's case and . . . if my statement got into the case . . . it would be very damaging to him." Nizamian added that his relation to Ty was "delicate" because he and Warner had recently discussed the possibility of doing business together and "I realized after speaking to Ty that it was a very important matter to him, and even though I didn't understand all of the particulars, I felt if he felt that strongly about it . . . maybe it would be best if I did not go." Nizamian did not say that Warner had threatened him, but "because of the seriousness in his voice and the importance to him, . . . I figured I'd just rather not get involved."

Testifying at the hearing on remand, Warner admitted that he had telephoned Nizamian in order to inquire whether he was going to testify but flatly denied Nizamian's version of the conversation. The district judge deemed Warner's testimony "incredible and false," said that he had lied under oath, and concluded that he had engaged in witness tampering. But on reconsideration she decided that she was "not prepared to find that Warner committed perjury. Nevertheless, it [i.e., she, the district court] adheres to the view that Warner was not credible and does not attribute his lack of credibility to memory lapse. As such, this finding, while still consistent with bad faith, may not be alone sufficient to support a conclusion of bad faith" (footnote omitted). We are uncertain what this means. The judge added that she had not found "that Warner `corruptly' persuaded Nizamian not to testify" and so she would not deem him guilty of witness tampering. Nevertheless she ruled that his "sanctionable misconduct" warranted the sanction of forfeiture of damages that she had imposed when she had thought him guilty of perjury and witness tampering. "Although Warner's actions were not criminal or quasi-criminal in nature, they interfered with Softbelly's ability to present its defense and thereby impaired an honest and true airing of the real facts."

This ruling was made before the retrial, at which, though Nizamian was present and willing to testify for Softbelly's, Softbelly's lawyer decided not to call him. The lawyer mistakenly believed that the jury was certain to find that Ty had not proved likelihood of confusion and therefore would lose regardless of how the issue of genericness, about which Nizamian would have testified, was resolved.

Ty's primary challenge to the sanction is that because it was punitive, its appropriateness had to be proved by clear and convincing evidence and not, as the judge thought, by a mere preponderance of the evidence. Indeed it was punitive. Softbelly's does not contend that it suffered any harm as a result of Warner's conversation with Nizamian other than having to pay the attorney's fees that it incurred in order to litigate the sanction issue. It does not argue that had he testified in the first trial the outcome would have been different. In this regard its failure to call him at the second trial and its abandonment of the defense that "Beanie Babies" is generic are telling.

Trying improperly to influence a witness is fraud on the court and on the opposing party, and the conventional rule, routinely invoked in cases in which a judgment is sought to be set aside under Fed.R.Civ.P. 60(b)(3) (that is, on the basis of "fraud . . ., misrepresentation, or misconduct of an adverse party"), e.g., Lonsdorf v. Seefeldt, 47 F.3d 893, 897 (7th Cir. 1995); Greiner v. City of Champlin, 152 F.3d 787, 789 (8th Cir. 1998); Smith v. Reddy, 101 F.3d 351, 353 (4th Cir. 1996); Rozier v. Ford Motor Co., 573 F.2d 1332, 1339 (5th Cir. 1978), is that fraud must be proved by clear and convincing evidence. But those cases are not compelling precedents in this case.

Rule 60(b)(3) is the lineal descendant of the equity rule that a court may alter or annul, because of fraud or undue influence, a written instrument (such as a contract or patent — but also a court's own judgment, see Hazel-Atlas Glass Co. v. Hartford-Empire Co., 322 U.S. 238, 244-45, 64 S.Ct. 997, 88 L.Ed. 1250 (1944)) only if the fraud or undue influence is proved by clear and convincing evidence. Herman MacLean v. Huddleston, 459 U.S. 388 n. 27, 103 S.Ct. 683, 74 L.Ed.2d 548 (1983); United States v. Maxwell Land-Grant Co., 121 U.S. 325, 381, 7 S.Ct. 1015, 30 L.Ed. 949 (1887). Rule 60(b)(3) is not applicable to this case, which does not involve the setting aside of a judgment. But some cases hold that any substantial sanction for misconduct in litigation must be proved by clear and convincing evidence. The principal case in this circuit is Maynard v. Nygren, 332 F.3d 462, 468 (7th Cir. 2003). But it involved Rule 37, and its soundness was questioned in Wade v. Soo Line R.R. Corp., 500 F.3d 559, 561 (7th Cir. 2007), where we pointed out that the Supreme Court has held that the standard for proving fraud under federal statutes is that of preponderance of the evidence rather than clear and convincing evidence. Herman MacLean v. Huddleston, supra, 459 U.S. at 388-90, 103 S.Ct. 683; Grogan v. Garner, 498 U.S. 279, 286-91, 111 S.Ct. 654, 112 L.Ed.2d 755 (1991). Wade suggests that Rule 37 can be compared to a statute — and it is a "statute" that lacks the special history of Rule 60(b)(3) that had made clear and convincing evidence the standard for motions under that rule.

The present case, however, involves not a ruling under Rule 37 but an exercise of a federal court's inherent authority to sanction misconduct in litigation before it; and a number of cases hold that the imposition of such a sanction (when indeed it is punitive and not merely compensatory) requires proof by clear and convincing evidence. See Shepherd v. American Broad-casting Cos., 62 F.3d 1469, 1476-78 (D.C. Cir. 1995), and cases cited there; also cases cited in Maynard v. Nygren, supra, 332 F.3d at 468. The logic of these holdings is that in the absence of a statute or rule, the exercise of judicial authority should be governed by traditional common law or equitable principles, such as the familiar principle that fraud must be proved by clear and convincing evidence. E.g., Barr Rubber Products Co. v. Sun Rubber Co., 425 F.2d 1114, 1120-21 (2d Cir. 1970); Shepherd v. American Broadcasting Cos., supra, 62 F.3d at 1477.

The tripartite division of burdens of proof — preponderance of the evidence, clear and convincing evidence, and proof beyond a reasonable doubt — has a certain logic. In an ordinary civil case, in which a prevailing plaintiff obtains only money, the consequences of error (which is always a risk in litigation) are symmetric: one party (the party that should have lost) is unjustly enriched, the other unjustly impoverished, by the same amount. At the other extreme, that of a criminal prosecution, the consequences to the contending interests are sharply asymmetric: a person unjustly convicted and sentenced to prison (or executed) incurs heavy costs of punishment, and the penal system incurs heavy costs of implementing punishment, whereas the only consequence of acquitting a guilty person is to reduce, usually rather modestly, the deterrent and incapacitative effects of the criminal law. In the intermediate case, that of a civil judgment for fraud, the consequences of error are slightly asymmetric. A judgment of fraud injures the defendant's reputation and may drive customers away and otherwise impair his ability to do business, and these costs are not a benefit to the plaintiff. The plaintiff gains a money judgment; the defendant loses a money judgment but incurs additional costs besides — therein lies the asymmetry.

But the asymmetry is attenuated when instead of suffering a judgment for having committed fraud in one's business activities, a litigant is sanctioned for fraud in the litigation itself. The sanction will often be written off by the larger community containing the defendant's peers — if the sanction is even noticed — as a mere battle scar of litigation. So we are led to doubt that there is any utility in insisting on proof by clear and convincing evidence in a case such as this, and getting entangled in disputes over whether Warner's conduct should be described as fraud and if not whether there should nevertheless be a category of litigation sanctions that require a heightened standard of proof.

We need not try to resolve our doubts. For just as the Constitution, while it has been interpreted to require proof beyond a reasonable doubt to convict in criminal case, also imposes (in the Eighth Amendment's cruel and unusual punishments clause) limitations on the severity of punishment, so the permissible level of sanctions for misconduct in litigation, except when prescribed by statute or rule, is, even when there is no heightened burden of proof, limited by notions of proportionality. E.g., Allen v. Chicago Transit Authority, 317 F.3d 696, 703 (7th Cir. 2003); Goss Graphics Systems, Inc. v. DEV Industries, Inc., 267 F.3d 624, 627 (7th Cir. 2001); Newman v. Metropolitan Pier Exposition Authority, 962 F.2d 589 (7th Cir. 1992); Nick v. Morgan's Foods, Inc., 270 F.3d 590, 597 (8th Cir. 2001); Zambrano v. City of Tustin, 885 F.2d 1473, 1480 (9th Cir. 1989). The limit was exceeded in this case. Cf. Barnhill v. United States, 11 F.3d 1360 (7th Cir. 1993). The district judge imposed what amounted to a large fine — nine times the amount necessary to compensate the victim fully (more, if Ty would be entitled to prejudgment interest on a damages award) — for what she described as "serious misconduct," even though (as in the parallel case of Lightning Lube, Inc. v. Witco Corp., 4 F.3d 1153, 1178-79 (3d Cir. 1993)) no harm was done by the misconduct beyond imposing a litigation expense on the opposing party that the misbehaving party is ready to make good. The finding of serious misconduct — especially since Ty does not contest it — stands as a black mark against Ty Warner's name, and has cost Ty substantial attorney's fees in fighting the sanction, as well as requiring it to cough up the $78,000 in attorney's fees incurred by Softbelly's in litigating the sanctions issue. Ty concedes that Softbelly's is entitled to those fees even though Softbelly's has failed in its quest for a greater sanction — dismissal of Ty's suit, as it first sought, or the $713,000 (or perhaps $1,028,000) forfeiture imposed by the district judge. Ty started Softbelly's on what has proved a wild goose chase, and must bear the consequences. But it has been punished enough for litigation misconduct that fortunately did not affect the course or outcome of the litigation.

We turn now to Softbelly's' appeal, where we can be brief. Softbelly's argues that a reasonable jury could not have found trademark infringement and that if there was infringement it was not willful. But it has abandoned the only argument that could have saved the day for it, which is that "Beanies" or "Beanie Babies" is the generic term for soft, plush objects, in the shape of animals, that are filled with bean-like materials to make the objects soft and floppy. If "Beanies" is generic — is, that is, "beanies" — it cannot be a legally protected trademark, and then Softbelly's is free to call its screen cleaners "Screenie Beanies." We expressed concern in our previous opinion that Ty's competitors might be rendered speechless unless they could call their soft, plush, bean-filled animalcules "beanies," but the narrowly drawn injunction should leave plenty of room for Softbelly's to designate its product crisply and clearly. As Ty's lawyer acknowledged at argument, Softbelly's could call its product a beanbag screen cleaner or even a screenie bean without infringement. Softbelly's itself has added "Cleanie Critter" to its lexecon, without challenge by Ty.

Softbelly's' abandonment of the argument that "Beanies" is generic leaves this a case in which a seller attaches a popular trademark to a product that is nearly identical to the trademarked one. E.g., Attrezzi, LLC v. Maytag Corp., 436 F.3d 32, 39 (1st Cir. 2006); Kos Pharmaceuticals, Inc. v. Andrx Corp., 369 F.3d 700, 714 (3d Cir. 2004); Nautilus Group, Inc. v. ICON Health Fitness, Inc., 372 F.3d 1330 (Fed. Cir. 2004). Many "Screenie Beanies" are identical in size, shape, and overall appearance to the corresponding "Beanie Baby" except for the chamois belly, which is invisible unless the animal is viewed from the bottom. It is true that the hang tag for "Screenie Beanies" differs from Ty's well-known red heart-shaped tag, being round and not red, but customers might well believe that Ty, having decided to make a screen cleaner rather than the conventional "Beanie Baby" toy, had changed the tag's appearance.

Softbelly's points out that "Screenie Beanies" are sold through different outlets from "Beanie Babies," are slightly more expensive, and have, of course, a different use. But the issue is only whether the designation "Screenie Beanies" on a nearly identical-looking product is likely to make a significant number of consumers think that Softbelly's product is actually a Ty brand; and the jury was entitled to answer the question in the affirmative. This is especially true because an increasing number of children use a computer at home and might wish to graduate from playing with "Beanie Babies" to cleaning their computer screens with the "adult" screen-cleaner version manufactured (they might well believe) by Ty and sold under the name "Screenie Beanie."

Softbelly's objects to the judge's having permitted Ty to present evidence of "Beanie" products that Ty marketed after "Screenie Beanies" entered the market. Obviously those products could not be used to show that the "Beanie Babies" trademark was in use before "Screenie Beanies" was, but they could be used as evidence of the likelihood that consumers would be confused about the source of "Screenie Beanies." Carnival Brand Seafood Co. v. Carnival Brands, Inc., 187 F.3d 1307, 1311 n. 4 (11th Cir. 1999). The greater the variety of products to which "Beanies" or "Beanie Babies" is attached, the likelier it is that consumers would assume that a new "Beanie" product that closely resembled "Beanie Babies" was also made by Ty.

Finally, the judge was on solid ground in finding that the infringement was willful; Softbelly's had chosen the name "Screenie Beanies" and the design of its screen cleaners with reckless disregard for the likelihood of consumer confusion. Its attempt to trademark "Screeniebeanies" had been turned down by the Patent and Trademark Office on the ground that it was potentially confusing.

To summarize, the grant of the injunction against Softbelly's is affirmed, but the case is remanded for the entry of a damages judgment of $713,000 against Softbelly's minus the attorney's fees incurred by Softbelly's in the sanction litigation. Whether the damages judgment should be augmented by prejudgment interest we leave to the district judge to decide in the first instance.

AFFIRMED IN PART, REVERSED IN PART, AND REMANDED WITH DIRECTIONS.