LEVAL, Circuit Judge:

Plaintiffs Lucretia Mali and the estate of Frederick Mali (hereinafter "Plaintiffs" or "the Malis") appeal from the judgment of the United States District Court for the District of Connecticut (Ellen Bree Burns, J.), entered after trial on the jury's verdict in favor of defendant Federal Insurance Company (hereinafter "Defendant," the "insurer," or "Federal"). The verdict and judgment denied the Malis indemnification under their insurance policy for the destruction of their barn by fire. The jury found the Plaintiffs had forfeited coverage under the terms of the policy by submitting fraudulent claims relating to the value of the barn and its contents. The Plaintiffs contend that the court abused its discretion in authorizing the jury to draw an adverse inference against them by reason of their failure to make disclosures demanded by the Defendant during the pretrial discovery proceedings. Federal cross appeals, demanding attorney fees and the return of a partial payment it made to the Plaintiffs on their claim. On Plaintiffs' appeal, we find no error in the instruction given to the jury. As for Defendant's cross appeal, we conclude Federal's claims are either forfeited or without merit.

BACKGROUND

A. The Malis' claim for destruction of their barn

The Malis owned property in Winsted, Connecticut, which included a barn converted for use as a residence. On April 1, 2005, the barn was destroyed by fire. The barn and its contents were covered by an insurance policy issued to the Plaintiffs by Federal. The Malis filed a claim with Federal for the loss of the barn and its contents. The policy included a provision denying recovery in the event the insured commits fraud in the assertion of a claim.

In July 2005, the Malis submitted to Federal an estimate of their claim, showing a loss of $1.325 to $1.5 million. Federal made three payments to the Malis totaling $72,665.48, for the loss of books, jewelry, a piano, and other items. Subsequently, in support of their claim, the Malis submitted a sketch of the layout of the barn showing that it had fourteen rooms, including a second floor with four rooms and a bathroom, and four skylights on the roof. Federal questioned the validity of the sketch as well as other factual predicates of the Malis' estimate, such as copper gutters, pine hardwood floors in the living room, a Garland stove in the kitchen, and four refrigerators. Federal declined to make further payments.

B. The Malis' suit on the claim

In August 2006, the Malis brought this suit. During pre-trial discovery Federal demanded, inter alia, that the Plaintiffs produce the names of household help who could furnish information as to the layout and contents of the barn, as well as any photographs of the interior of the barn, and in particular of the second floor. The Malis responded that they had no photographs of the second floor. They also did not identify any household help. The Malis meanwhile increased their loss estimate to $2.299 million, based on their assertion that the barn contained $632,137.65 worth of ceramic tile.

At trial, Lucretia Mali testified, consistent with the Plaintiffs' earlier submission, that the barn had fourteen rooms, including four rooms on the second floor, and that the barn contained four skylights, ceramic tiling, a Garland stove, four refrigerators, a back room, and wide plank wood floors in the main living space.

Among the witnesses called by the Plaintiffs in support of their claim was Helaine Fendelman, an antiques appraiser whom Lucretia Mali had hired to estimate the value of various items that were allegedly destroyed in the fire. Fendelman testified that in the course of her work, she was shown photographs depicting both the items and the interior of the barn. Her direct testimony included the following:

Federal's cross-examination of Fendelman on the same day included the following:

Fendelman's testimony that she was shown a photograph of the second floor was apparently contradictory to the Malis' earlier assertion during pre-trial discovery that they had no such photographs.

Lucretia Mali later testified that she did not possess any photographs of the second floor. She explained that she had provided Fendelman with photographs of items that were on the second floor at the time of the fire, but that those photographs had been taken long before the objects were moved to the barn, and did not show the barn's second floor.

After the parties rested, Federal moved for an adverse inference jury instruction as a sanction for the Plaintiffs' discovery misconduct, arguing that Fendelman's testimony showed that the Malis had withheld a photograph of the second floor of the barn. The Plaintiffs responded that Fendelman was mistaken in testifying that she had seen photographs of the upstairs of the barn. The Plaintiffs then sought leave to recall Fendelman to correct her testimony, asking alternatively that the court not give the requested adverse inference instruction, or that, if given, the instruction not state that the evidence "tended to show" that Plaintiffs withheld evidence. The court denied the Plaintiffs' application to recall Fendelman (in part because such testimony would not be appropriate rebuttal) and expressed the view that an adverse inference instruction was "appropriate," explaining that "there is evidence, which, if believed by the jury, tends to show that there was a photo of the upstairs of the barn house, that such photo would be relevant to issues in the case and that such photo was in the exclusive possession and control of Lucretia Mali at the time when it was clear litigation was likely. Ms. Mali has failed to produce any such photo."

On summation, both sides presented arguments concerning whether the jury should draw an inference against the Plaintiffs based on Fendelman's testimony that she saw a photograph of the upstairs of the barn. The Plaintiffs pointed out that the existence of an upstairs photograph had been expressly refuted by Lucretia Mali, and argued that no such photograph exists. Federal argued that the jury should credit Fendelman's testimony that she had been shown such a photograph, and on that basis should draw an adverse inference against the Plaintiffs to the effect that the upstairs of the barn consisted of only one room (and not four as the Plaintiffs contended).

In the course of its jury instructions, as part of the instruction on circumstantial evidence, the court charged the jury as follows (substantially in the form suggested by the Plaintiffs):

The jury, as noted above, found for the Defendant Federal. On a Special Verdict form, the court asked the jury, "Do you find that the Defendant proved, by a preponderance of the evidence, that the Plaintiffs violated the fraud and misrepresentation clause of the Policy?" The jury answered, "Yes."

Following trial, Federal moved for attorney fees and for equitable relief in the form of a refund of the $72,665.48 it had paid out to the Malis in September 2005. The court denied both motions. It determined that attorney fees were not appropriate because the alleged bad faith conduct was not sufficient to warrant fee shifting. As for the return of the moneys paid, the court concluded that Federal's claim should have been pled as a compulsory counterclaim and could not be brought as a post-trial motion.

DISCUSSION

A. The permissive adverse inference instruction was appropriate

The Malis contend the judgment should be vacated and a new trial ordered because the court imposed a sanction without first making the findings necessary to justify the sanction. Their argument is based on a faulty premise. The court did not impose a sanction on the Plaintiffs. It merely instructed the jury, as a part of its explanation of circumstantial evidence, on inferences the jury was free to draw depending on the jury's findings. The court was not required to make any predicate findings to give such an instruction.

The Malis correctly quote our opinion in Residential Funding Corp. v. DeGeorge Financial Corp., 306 F.3d 99, 107 (2d Cir. 2002) to the effect that before imposing a sanction consisting of "an adverse inference instruction based on [a party's] destruction of evidence," the court must find facts that justify the sanction. The Malis are correct, furthermore, in asserting that the district court did not make findings that would be necessary predicates to the imposition of a sanction — most prominently a finding that the Plaintiffs in fact showed Fendelman a photo of the upstairs of the barn, which they failed to produce in discovery.

But Residential Funding dealt with a very different set of circumstances. In Residential Funding, the defendant claimed that, during the pretrial discovery process, the plaintiff Residential had breached its discovery obligations by failing to produce e-mails and backup tapes. DeGeorge moved for a sanction in the form of an instruction to the jury that "it should presume the emails from October to December of 1998, which have not been produced, would have disproved [Residential]'s theory of the case." Residential Funding, 306 F.3d at 105 (emphasis added). The district court declined to impose the sanction, finding that defendant De-George had failed to demonstrate facts needed to justify the sanction. On appeal, we approved the broad proposition that a trial judge may not impose a sanction as a punishment for misconduct without making findings that support the propriety of the punishment.1

The Malis rely on this proposition from Residential Funding in arguing that the district court could not properly impose the sanction of an "adverse inference instruction" without making necessary findings, which the district court did not make. The confusion that underlies the Malis' argument results from the fact that the words "adverse inference instruction" can be used to describe at least two different sorts of instructions.

One type of adverse inference instruction — the sort that was the subject of our Residential Funding opinion — is a sanction, or in other words, a punishment for misconduct. It is axiomatic that a court may not punish without finding misconduct that merits the punishment. Most commonly, such an instruction is given as a sanction with respect to misconduct that occurred outside the presence of the jury during the pretrial discovery proceedings, often consisting of a party's destruction of, or failure to produce, evidence properly demanded by the opposing party. Fed. R.Civ.P. 37 authorizes a wide range of sanctions for such discovery abuses. For example, if the district court in our case had determined (which it did not) that the Malis had photos of the second floor and wrongfully withheld them, it might simply have told the jury those facts and nothing more; or it might have added that the jury could, but need not, draw inferences against the Malis based on those facts; or, as requested in Residential Funding, that the jury should draw adverse inferences against the Malis based on those facts; or that the jury should render a verdict for the Defendant. See Fed.R.Civ.P. 37(b)(2)(A). Before imposing any such sanction, the court would need to make findings that justified the sanction.2

A second, fundamentally different, adverse inference instruction is one that simply explains to the jury, as an example of the reasoning process known in law as circumstantial evidence, that a jury's finding of certain facts may (but need not) support a further finding that other facts are true. Such an instruction is not a punishment. It is simply an explanation to the jury of its fact-finding powers. Instructions of this nature are very common. An example that is routinely given is the instruction that, if the jury finds a witness has lied on one subject, it may (but need not) find on that basis that the witness has lied on other issues as well. The court need not find any facts to justify such an instruction, which leaves all the fact finding to the jury without encroachment by the court. See United States v. Amuso, 21 F.3d 1251, 1259-61 (2d Cir.1994) (upholding instruction that permitted, but did not require, the jury to infer that the defendant believed he was guilty because he fled the police); Leonard B. Sand, et al., 4 Modern Federal Jury Instructions-Civil ¶ 75.01 (jury instruction explaining the concept of inferences); see also County Court of Ulster County v. Allen, 442 U.S. 140, 157, 99 S.Ct. 2213, 60 L.Ed.2d 777 (1979) (noting, in the criminal law context, that permissive inference instructions are common).

The instructions here given to the jury were of the latter sort. The court did not direct the jury to accept any fact as true. Nor did it instruct the jury to draw any inference against the Plaintiffs. The court left the jury in full control of all fact finding. It did no more than explain to the jury that in the event it found one fact to be true, it was free, but not required, to infer another fact from the first. While such an instruction is indeed an "adverse inference instruction," in that it explains to the jury that it is at liberty to draw an adverse inference, it is not the sort of punitive adverse inference instruction that we discussed in Residential Funding. It is not a sanction. It is no more than an explanation of the jury's fact-finding powers.

It is true that in requesting an adverse inference instruction, Federal argued that it should be done as a sanction for the Plaintiffs' failure to produce the photo. Nonetheless, in explaining why it would give the instruction, the court did not say it was doing so as a sanction. The court merely said that an adverse inference instruction was "appropriate" because of the conflicting evidence as to whether the Malis in fact showed Fendelman a photo of the upstairs. Furthermore, the instruction the court gave was essentially the version suggested by the Plaintiffs, which did not instruct the jury to accept any disputed fact as true, or to draw any adverse inference, but left all fact finding entirely within the jury's discretion.

In short, the passages from Residential Funding on which the Plaintiffs rely related to a different sort of adverse inference instruction — an instruction given as a sanction for misconduct and not one that simply explains to the jurors inferences they are free to draw in considering circumstantial evidence. The Plaintiffs' contention on appeal is thus without merit.

B. Federal is not entitled to attorney fees

We reject Federal's contention that it is entitled to recover its attorney fees from the Plaintiffs. The American rule is that, absent a statute providing otherwise, the parties to litigation pay their own attorney fees regardless of outcome. See Sierra Club v. U.S. Army Corps of Eng'rs, 776 F.2d 383, 390 (2d Cir.1985). There is some support for a narrow exception to this rule for cases that have been prosecuted in bad faith. See Eisemann v. Greene, 204 F.3d 393, 395-96 (2d Cir.2000). For such cases, we have said that the order to shift fees must be justified by a finding supported by clear evidence that (1) the offending party's claims were entirely without color, and (2) the offending party's claims were made in bad faith. See id. at 396. Furthermore, the trial court has very broad discretion to deny an application to shift fees. See id.

Federal made three arguments to the district court in support of its entitlement to attorney fees: that the action was commenced in bad faith, that the Malis failed to produce the photograph of the second floor of the barn, and that they failed also to provide the name of any household help who could have testified to the layout of the barn. On appeal, Federal adds two more arguments: that during discovery the Malis fraudulently increased their estimate by over $600,000 (due to the claimed ceramic tiling), and that they gave perjured testimony about the existence of the skylights and the Garland stove. None of these arguments support overturning the district courts's denial. The contentions that were not made to the district court, relating to ceramic tiling, skylights and a Garland stove, were forfeited by failure to raise them below. As for the claims of bad faith in failing to produce a photograph of the second floor or to furnish the names of household help, there was no finding by the district court that such matter was available and was wrongfully withheld. This court has no basis for making such a finding. Federal's contention that the action was brought in bad faith is also wrong. It is not disputed that the Malis had a barn covered by insurance which burned down. There was no impropriety in bringing suit for the value of the barn, even if the Plaintiffs committed fraud as to its value.3

We do not decide whether the district court would have been within its discretion had it granted Federal's motion for attorney fees. But it is clear the court did not abuse its discretion in denying that unusual remedy.

C. Federal is not entitled to equitable relief

Federal contends that the trial court erred in denying its post-trial motion for equitable relief to recover the payments it made to the Malis in September 2005, which totaled $72,665.48. We disagree. Federal does not contend that those payments were themselves procured through fraud. However, because the jury's finding that the Malis committed material misrepresentations has absolved Federal of all obligation to pay the Malis' insurance claims, Federal argues that it should be reimbursed for its prior payments.

Fed.R.Civ.P. 13(a) provides that "[a] pleading must state as a counterclaim any claim that — at the time of its service — the pleader has against an opposing party if the claim ... arises out of the transaction or occurrence that is the subject matter of the opposing party's claim." A counterclaim that is not timely pled is subsequently barred. See Baker v. Gold Seal Liquors, Inc., 417 U.S. 467, 469 n. 1, 94 S.Ct. 2504, 41 L.Ed.2d 243 (1974). Federal's answer in the district court did not assert a counterclaim for restitution, and Federal never sought to amend that pleading to include such a counterclaim.

Federal makes two arguments to avoid waiver. Neither is successful. First it argues that because the policy did not become void until the jury found the Malis had committed fraud, the claim had not accrued and Federal could not have asserted it prior to the jury's verdict. This is simply incorrect. Federal claimed from the outset that the Malis committed fraud and that their fraud voided the policy. It did not need to await the jury's vindication of that claim to add a counterclaim for reimbursement of the initial payments. Under Connecticut law a claim accrues "when [a party] first could have successfully maintained an action." Polizos v. Nationwide Mut. Ins. Co., 255 Conn. 601, 609, 767 A.2d 1202 (2001) (internal quotation marks and citation omitted).

Second, Federal contends that the district court had inherent power to impose equitable relief irrespective of Rule 13(a). But even assuming arguendo that the court had authority to grant the relief, it does not follow that the court abused its discretion in declining to give Federal such extraordinary relief.

CONCLUSION

The judgment of the district court is AFFIRMED.