This is a consolidated appeal from a judgment entered on April 21, 1988, by the United States District Court for the Southern District of New York, Robert L. Carter, Judge, following our remand for the recalculation of damages. Ostano Commerzanstalt v. Telewide Systems, Inc., 794 F.2d 763 (2d Cir.1986). In the first appeal, we affirmed Judge Carter’s holdings as to liability for fraud and breach of contract. Id. (affirming as to liability Ostano Commerzanstalt v. Telewide Systems, Inc., 608 F.Supp. 1359 (S.D.N.Y.1985)). After the remand, Judge Carter conducted a four-day trial on damages and ordered the entry of a second amended judgment. Ostano Commerzanstalt v. Telewide Systems, Inc., 684 F.Supp. 1172 (S.D.N.Y.1988).
Telewide Systems, Inc. (“Telewide”), appeals the judgment against it in the amount of $6,120,367.261 for breach of contract. Bernard L. Schubert appeals the judgment against him for damages for fraud of $526,819.082 and punitive damages of $500,000. Telewide, Schubert, and their counsel, the firm of Hall, Dickler, Lawler, Kent & Friedman, appeal a $153,-087 award of attorneys’ fees that was entered 3°™% and severally against all of them.
Telewide and Schubert argue that it was improper for the district court to grant an amendment adding a new plaintiff, TSC Technische Systeme Consult GmbH & Co. Communication International KG (“TSC”), after the close of testimony on the remand, and they argue that the assignment of the claim of plaintiff Ostano Commerzanstalt (“Ostano”) to TSC precludes Ostano from recovering any damages. They also argue that the district court improperly calculated the measure of damages for breach of contract, fraud, and punitive damages and that the district court improperly excluded testimony of the validity of the films’ copyright under German law. Finally, Telewide, Schubert, and their law firm, which has appealed separately, argue that the district court erred in assessing attorneys’ fees.
FACTUAL BACKGROUND
Ostano and Dr. Herbert Jovy began this action in 1982 alleging breach of contract, breach of warranty, and fraud in connection with an agreement for the licensing of certain old feature films in Europe and Africa. Although we presume the reader’s familiarity with the prior opinions in this case, we will present a brief summary of the facts. Plaintiff Dr. Herbert Jovy is affiliated with three foreign companies that were involved in the transaction that gave rise to this lawsuit. Dr. Jovy’s wife owns plaintiff Ostano, his wife and son, Hanns-Arndt Jovy, own plaintiff TSC, and Dr. Jovy also has a relationship with a third company, TT Telefilm Trading, Ltd. (“TT Telefilm”). Defendant Bernard Schubert is the president and sole shareholder of defendant Telewide, which is an American company. In 1980, Video Communications Inc. (“VCI”), an apparently independent *644company, bought film rights from Telewide and sold them to Ostano. The license was for the right to distribute for television twenty-six feature films in four German-speaking countries (East and West Germany, Austria, and Switzerland) and four other countries (France, Belgium, the Netherlands, and Luxembourg). Also in 1980, Ostano sublicensed its rights for the German-speaking countries to TT Telefilm, and TT Telefilm sublicensed those rights to TSC. In 1981, the plaintiffs sued VCI alleging various problems with the license. When that suit was settled, VCI assigned its rights in its contract with Telewide to Ostano. The present suit was filed in 1982. In 1983, Ostano assigned its remaining contract rights (those in the non-German-speaking countries) and its claims against the defendants to TSC. 684 F.Supp. at 1173. Due to various difficulties that were the source of the district court’s holding on liability, the plaintiffs were never able to distribute most of the films. A few, however, were licensed to West German broadcasters. 794 F.2d at 766.
After the first trial, the district court held Telewide liable for breach of contract and warranty in the sum of $4,262,021.75. The court calculated damages by speculating that the value of a license could be computed simply from the number of television sets within the territory for which the license was granted. Judgment was also granted against both Telewide and Schubert for fraud, false representation, and fraudulent breach of warranty in the same amount. The district court further held Telewide and Schubert liable for prejudgment interest from May 20, 1980, awarded punitive damages jointly and severally in the sum of $500,000, and held plaintiffs entitled to an award of attorneys’ fees and costs. 608 F.Supp. at 1369.
On the first appeal, we agreed that Tele-wide was liable for breach of contract and that Telewide and Schubert were both individually liable for fraud, but we found the district court’s damage calculation unsatisfactory. 794 F.2d at 766-68. We also pointed out the necessity of differentiating between fraud and breach of contract damages, id. at 766, and held that the district court could not award damages against Schubert for fraudulent breach of warranty because he was not a party to the contract, id. at 767. We warned that Ostano should not receive a double recovery, holding that it was improper for the district court to add the price that Ostano paid for the license to the damages for breach of contract. Id. at 767-68. Finally, we remanded the issue of punitive damages, requiring that any award be based solely on the deliberate and willful nature of the fraud and misrepresentation, and we noted that on remand sanctions might be considered. Id. at 768.
After a four-day trial on remand, Ostano and Jovy moved to add as an additional plaintiff TSC, to which they had assigned their rights to the license in 1983. On January 22,1988, the district court granted the motion, thereby conforming the pleadings not only to the evidence but also to the original pretrial order.
Due to the controversy over the addition of TSC, a description of the pretrial order will be helpful. The pretrial order had many references to TSC’s role as a claimant. It stated that “[i]n November 1980, Ostano sub-licensed the distribution of the films in German-speaking countries to a Munich affiliate named [TSC].” It also stated that plaintiffs’ ease would be that Telewide and Schubert had, among other things, “interfered with Ostano’s and TSC’s access to prints and pre-print material needed to make prints,” and that “both Ostano and TSC are owned by Dr. Jovy’s wife.” The order referred to TSC’s contract with Polygram in Hamburg, West Germany, for certain of the films, to Org-team, a subsidiary of Radio Luxembourg, to which Ostano and TSC were attempting to market the films, to TSC’s loss of the entire contract with Polygram, and to the fact that negotiations with Orgteam had had to be discontinued. It also referred to the claim that “Ostano and TSC had been unable successfully to market the films in the Territory” and that lost profits of at least $1,426,195 would be shown “by virtue of lost sales by Ostano and TSC in Germany, Austria, Switzerland, Holland, Luxem*645bourg, Belgium and France.” The description of the defendants’ case, on the other hand, included a general claim that plaintiffs had failed to join indispensable and necessary parties and were not the real parties in interest.
The trial exhibits listed in the pretrial order also included many references to TSC: No. 47, an October 29, 1982, letter from TSC to Filmlager Berlin; No. 52, an undated contract between TSC and WDR regarding “Marry Me Again” and other films; No. 54, a contract dated October 29, 1981, between TSC and Bayerischen Rund-funk; Nos. 57 and 58, each consisting of a one-page list of the subject films by TSC with handwritten notations or with German titles; No. 60, a sixty-four-page list of films by TSC; No. 61, a six-page list of films by TSC; and No. 67, an agreement dated December 18, 1980, between TT Telefilm, as licensor, and TSC. Finally, two of the issues of fact to be determined by the court, Nos. (i) and (j), referred to TSC.
At the hearing on damages there was evidence of the prices of films shown on European television, evidence of expenses and revenues that the plaintiffs accrued in seeking to license the Telewide films, and evidence of the value of the Telewide films. One of the witnesses for the plaintiffs, Dr. Peter Sczygiol, was a representative of the publishing house of Springer AG who had negotiated with the plaintiffs to purchase the rights to license some of the Telewide films in seven of the countries. Dr. Jovy’s son, Hanns-Arndt Jovy, also testified for the plaintiffs. The defendants called Laurence Gershman, a former MGM executive, and a fourth individual whose testimony the court found useless. 684 F.Supp. at 1173. The district court found that the defendants’ evidence was only “marginally at variance” with the plaintiffs’. Id. at 1173-74.
West Germany was apparently the plaintiffs’ most lucrative potential market. According to the witnesses and to Variety and TV World, which were acknowledged to be authorities on rating and pricing films with respect to West Germany, in that country each film was worth $50,000 to $59,000 (according to Variety), $50,000 to $75,000 (according to TV World), $63,000 (according to Jovy), or $60,000 to $75,000 (according to Gershman). Dr. Sczygiol gave figures of $126,000 to $189,000 per film for seven of the countries (all except East Germany), with the prices subject to a 15% package discount. The prices in the other countries were for the most part calculated according to Variety and TV World, but there was also live testimony as to the prices in Austria, Switzerland, Belgium, France, Luxembourg, and the Netherlands. Id. at 1174.
The court concluded that “the price in the territory ranged from $105,700 to $189,000 per film for all the countries involved. This means that the 26 films were valued at $2,748,200 to $4,862,000,3 averaging $3,831,000 for the 26-film package.” Id. To calculate the benefit-of-the-bargain damages on the breach of contract and warranty claims, the court took $3,831,000, the average (or mean) above noted, as the value to be placed on the license for the territory consisting of the eight European countries. The court subtracted from that $177,549.09, the plaintiffs’ net revenues from the sales of the films to small broadcasters, leaving the benefit-of-the-bargain damage award at $3,653,550.91, to which was added prejudgment interest calculated from May 13, 1980. Id. at 1175-76.
As to the fraud claim, the court held that Ostano and TSC were entitled to recover the consideration paid for the fraudulent license, plus reasonable expenses incurred in any attempt to market the films, less any revenues earned in the process. Using an exchange rate of fifty cents for each Deutschmark, the court figured that the amount paid for the license was $512,-021.75, that expenses were $87,245.43, totaling $599,267.18, and that gross revenues equaled $264,794.52. Thus the court held plaintiffs entitled to recover on their fraud claims $334,472.66, plus prejudgment interest of 9% on the $87,245.43 expenses, calculated from January 1, 1985, and prejudgment interest of 9% on the remaining *646amount, calculated from May 13, 1980. Id. at 1176. Punitive damages in the sum of $500,000 were awarded against Schubert on the basis that “Schubert entered this transaction from the outset with a clear and blatant intent to defraud.” Id. The court noted that “the demeanor and acts of the defendant at trial may be considered ‘as bearing on whether there is a need for punishment of the defendants and deterrence of like conduct by others who may be in similar circumstances in the future.' ” Id. (quoting Hall v. Ochs, 623 F.Supp. 367, 377 (D.Mass.1985), aff'd in part and rev’d in part, 817 F.2d 920 (1st Cir.1987)). For good measure, the court added that “[t]he conduct at trial makes clear the deliberate, premeditated nature of the fraud perpetrated on plaintiffs.” Id. at 1176-77.
The court awarded the plaintiffs $153,-087 in attorneys’ fees to be paid by Schubert, Telewide, and the defendants’ attorneys, the law firm of Hall, Dickler, Lawler, Kent & Friedman, jointly and severally. Id. at 1177.
DISCUSSION
I. The Addition of TSC as a Plaintiff After the Close of the Trial on Damages. Appellants argue that the district court abused its discretion in adding TSC as a plaintiff after the close of the trial on damages. They first argue that the district court, on remand, should not have gone beyond this court’s instructions. This argument borders on the frivolous. Although remands with specific mandates limit the trial court to the imperative of the mandate, see W.R. Britton v. Dowell, Inc., 243 F.2d 434, 434-35 (10th Cir.1957), our mandate did not preclude the addition of TSC.
We affirm the district court’s decision because, as the recital of the terms of the pretrial order indicates, the defendants were at all times on notice that TSC was a sublicensee of Ostano. Federal Rule of Civil Procedure 15(b) permits the amendment of the pleadings to conform to the evidence. Rule 21 authorizes the district court to order the addition of a party at any time “on such terms as are just.” The addition of TSC was proper under both of the rules. Judge Charles Clark, who served as Reporter to the Advisory Committee on Civil Procedure of the Supreme Court from 1935 to 1956 and who was called the “father” of the Federal Rules by Judge Harold Medina, see M. Schick, Learned Hand’s Court 30-31 & n. 81 (1970), wrote for the court in SEC v. Rapp, 304 F.2d 786, 790 (2d Cir.1962), that Rule 15(b) is “mandatory, not merely permissive,” in requiring that issues that are tried, though not raised in the pleadings, be treated as if they were raised in the pleadings. As he said, “Indeed, formal amendment is needed only when evidence is objected to at trial as not within the scope of the pleadings,” and he referred to “[t]he well-known objective of the rule that cases should be decided on resolution of the actual dispute between the parties, rather than on the paper pleadings filed at the inception of suit.” Id. Given the many references to TSC in the pretrial order, the defendants could not have been prejudiced by the plaintiffs’ failure to join TSC earlier. Accordingly, we find unhelpful the cases cited by Telewide and Schubert which deal with questions of timeliness, prejudice, and bad faith under Rule 21. We also find that amendment after remand and a second trial is permissible. Pleadings can be amended after remand. See C. Wright & A. Miller, 6 Federal Practice and Procedure § 1494, at 475 (1971). We see no earthly reason to prevent amendment after the second trial.
II. The Calculation of Contract Damages. The appellants argue that the district court erred in admitting evidence of the value of some of the films based on contract negotiations and in calculating the value of the films in the license territory on the basis of an average. The first argument is that Dr. Sczygiol’s testimony as to negotiations should not have been admitted because he did not have sufficient authority to negotiate or execute a contract on behalf of his firm, Axel Springer AG. Moreover, it is said that Dr. Sczygiol’s testimony related to only ten Telewide films, of which only three were films as to which the district court found rights lacking. Sczygiol, indeed, testified that, subject to *647approval, he was authorized to purchase ten Telewide films on behalf of Springer for the eight countries: nine films for $126,000 each and one, “Blue Gardenia,” for $189,000, all subject to a customary 15% package discount. 684 F.Supp. at 1174-75. But his authority to negotiate and the scope of the failed transaction are irrelevant. His testimony was properly admitted to corroborate other testimony, not to prove that the plaintiffs could have profited by licensing to him.
Our review of the evidence convinces us that the award of benefit-of-the-bargain damages must be changed. We have reviewed Sczygiol’s testimony regarding seven of the countries. As to West Germany, Hanns-Arndt Jovy alluded to a $63,000 price4 as standard for the sale of television broadcasting rights, to the two national West German broadcasters, with smaller regional stations paying less than half that much. Laurence Gershman, the defendants’ expert, said that the two West German national broadcasters presently pay about $60,000 to $75,000 for West German broadcasting rights and that there was no reason to doubt that $63,000 was a standard price for West German rights in 1980. Neither Jovy nor Gershman testified as to East Germany, but Variety reported $6,000 to $10,000 and the defendants’ expert, Gershman, agreed that Variety’s reported prices were “indicative,” even though not “authoritative.” TV World reported East German prices that are generally the same as reported in Variety. For France, Variety reported a price per film of $30,000 to $40,000, TV World reported a price of $30,-000 to $50,000, and Gershman testified to a price of $40,000 to $45,000. For Belgium, Variety reported a film price ranging from $5,000 to $21,000, Jovy testified to $4,500, and Gershman testified to $4,000 to $5,000. For Luxembourg, Variety, TV World, and Gershman5 testified to a price of $5,000 to $6,000 and Jovy to a price of $5,000. For the Netherlands, Variety and TV World reported a price of $7,500 to $8,500, and Gershman testified to a price of $4,000 to $6,000. For Switzerland, the publications reported $4,000 to $9,000, and Jovy reported $6,000. For Austria, Variety reported $2,700 to $5,000, TV World reported $2,750 to $5,000, and Jovy reported $7,500. See 684 F.Supp. at 1174.
Thus, for all eight of the countries in the territory, Variety’s price for the distribution of one film ranged from $110,200 to $158,000, with a mean of $134,350, and TV World’s price for seven of the countries ranged from $105,250 to $163,500, with a mean of $134,375. Gershman’s range, which did not include East Germany, Austria, or Switzerland, was $113,000 to $137,-000, with a mean of $125,000. Faced with such similar testimony, we have decided to use the plaintiffs’ testimony as our basis for the award. Jovy’s testimony did not include prices in East Germany, France, or the Netherlands, but if one added to his estimates Gershman’s low estimates for the latter two countries and the Variety and TV World low estimate of $6,000 for East Germany, then the mean value per film in the territory would be $136,000. Using $136,000 per film, which, in view of its similarity to the average of Variety’s range, would seem a fair price in relation to most of the twenty-six films involved, we come to a preliminary calculation of benefit-of-the-bargain damages of $3,536,000. Yet the district court arrived at the figure of $3,831,000 for the twenty-six film package.
The district court found that the prices ranged from $105,7006 to $189,0007 per film and averaged those two figures. The court multiplied $147,350, the average price *648of the films, by twenty-six, and reached the total of $3,831,0008 for the package. We think this is mixing apples and oranges. Only one film, “Blue Gardenia,” was estimated to be worth $189,000. All of the other films were quoted at lower prices, and indeed Sczygiol’s testimony, which appellants would have excluded, actually helps them because he would have priced at $126,000 all nine of the other films he discussed. It is ironic that the testimony that helps appellants most is the very testimony that they believe should have been excluded. Moreover, we believe that a 15% package discount, such as Sczygiol mentioned, is appropriate. Our calculation of benefit-of-the-bargain damages, which are based on the market value of the films, presumes that the films would be resold without significant further expenses, as might occur in a package sale. If one takes into account a package discount of 15%, which Judge Carter did not do, the total damages would be reduced from the $3,536,000 that we calculated above to $3,005,600, a figure which seems to us reasonable. Of course, our own calculation does not yet account for the higher value of “Blue Gardenia,” so we add the sum of $45,050, representing the higher value of “Blue Gardenia” ($189,000 less $136,000) minus its own 15% discount. Finally, we must, like the district court, subtract the net revenues that the plaintiffs managed to earn by marketing a few films. Subtracting $177,549.09 leaves an award of $2,873,-100.91. Any award beyond these figures would be speculative.
Appellants also argue that the evidence clearly established that, contrary to Sczy-giol’s testimony, the prices he negotiated were in Deutschmarks, rather than dollars. We think that the evidence established that Sczygiol’s testimony as to dollars can stand because he negotiated for seven countries (all but East Germany) and because the testimony of Jovy and Gershman as well as the listings in Variety and TV World come very close to Sczygiol’s lower figure.
We thus reduce the contract damages recoverable against Telewide to $2,873,-100.91, which will accordingly require a reduction in the amount of prejudgment interest.
III. Ostano’s Recovery of Out-of-Pocket Damages. Appellants also argue that Ostano should recover only its out-of-pocket losses caused by the fraud committed by Telewide and Schubert, and that is exactly what we said in our previous ruling. The cost of the license was $512,021.75. But Ostano received something of value in exchange since some of the films in the package were in fact licensed, as we held, to German broadcasters. 794 F.2d at 766. The appellants argue that because Ostano was paid $520,149 for the rights in the German-speaking region by TT Telefilm, Ostano suffered no out-of-pocket loss. But the sublicense to TT Telefilm was followed by a further pass-through of those rights to TSC, another affiliate of Ostano. This point was never made at the previous trial, though we note that defendants’ first brief specifically referred to the sublicense to TT Telefilm followed by sublicense to TSC. See Brief for Appellants at 6, 794 F.2d 763 (2d Cir.1986). Although TSC obtained some revenues from sales to third parties, the plaintiffs are entitled to recover the damages that they did incur.
Damages for fraud include the costs incurred in preparing for, performing, or passing up other business opportunity, Fort Howard Paper Co. v. William D. Witter, Inc., 787 F.2d 784, 793 n. 6 (2d Cir.1986), as well as costs incurred in making reasonable efforts to mitigate damages, see, e.g., Lanite Sales Co. v. Elevens Corp., 205 Misc. 303, 308-09, 128 N.Y.S.2d 182, 188 (Sup.Ct.1954). The evidence here was that the plaintiffs paid $512,021.75 for the Telewide films, 608 F.Supp. at 1362, and the court found additional allowable expenses of $87,245.43, 684 F.Supp. at 1176. The district court, following our instructions exactly, then subtracted the gross revenues obtained by plaintiffs in marketing the films, producing the correct net recoverable out-of-pocket expenses of $334,472.66.
*649IV. Double Recovery. It is true, as we said in our first opinion, that the plaintiffs cannot recover both benefit-of-the-bargain damages for breach of contract and warranty and out-of-pocket expenses for fraud. Such a double recovery would put them in a better position than they would have been in had the contract been satisfactorily performed. At the same time, because Schubert is not a party to the contract, only Telewide is liable on the larger, contract-based claim. Both Schubert and Telewide are liable on the fraud claim,9 but damages were awarded only against Schubert.
In order to prevent double recovery of compensatory damages, we follow the suggestion made by appellees. The full payment of the contract award, which is the larger of the two, plus the attorneys’ fees which will be discussed below, shall be deemed a satisfaction of the smaller compensatory award for fraud. Schubert in no event will be required to pay more than the amount awarded against him for fraud, punitive damages, and attorneys’ fees, plus interest. All payments of compensatory damages by either defendant should be first credited to the larger (contract) award, as is the rule in respect to joint tortfeasors. See Kassman v. American Univ., 546 F.2d 1029, 1033-35 (D.C.Cir.1976). Thus, if the $2,873,100.91 (plus interest) award for contract damages is satisfied first, Schubert’s $334,472.66 (plus interest) liability for fraud damages should be deemed satisfied. Schubert will remain individually liable for the $500,000 punitive damage award against him until he pays it, because the punitive damages are not compensatory and could not cause any double recovery. Payments that Schubert makes should be credited to compensatory damages first. Once the $334,472.66 (plus interest) is paid, Schubert’s payments should go first to the attorneys’ fees and thereafter to the punitive damages award.
V. Punitive Damages. The award of punitive damages rests on a district court finding, which we do not find clearly erroneous, that Schubert entered the transaction with the clear and blatant intent to defraud. 684 F.Supp. at 1176-77. There was evidence that when Schubert signed the Telewide license, he knew that Telewide lacked European distribution rights to several of the films. 608 F.Supp. at 1364-66.
Nor do we agree that there must be acts aimed at the public to support an award of punitive damages in a fraud case. Rather, punitive damages may be awarded when fraud is gross, wanton, or willful, whether or not directed at the public generally. See Borkowski v. Borkowski, 39 N.Y.2d 982, 355 N.E.2d 287, 387 N.Y.S.2d 233 (1976) (mem.); see also Roy Export Co. Establishment of Vaduz v. CBS, Inc., 672 F.2d 1095, 1106 (2d Cir.), cert. denied, 459 U.S. 826, 103 S.Ct. 60, 74 L.Ed.2d 63 (1982) (under New York law, punitive damages are appropriate where wrong is aggravated by recklessness or willfulness, whether or not directed at public generally).
VI. The Admission of Evidence Concerning Aspects of Copyright Law in the Federal Republic of Germany. Appellants argue that the court improperly excluded testimony regarding the copyright protection Germany afforded the films. Appellants indicated to the district court that one Dr. Gunter Poll would testify that under a copyright agreement between the United States and Germany, films original*650ly copyrighted in the United States are afforded the same copyright protection as films of German origin. Dr. Poll would also have testified that German law protects copyrights for the life of the author plus seventy years, even if copyright protection has expired in the United States. But our remand was on the issue of damages, and the appellants are precluded by the law of the case from raising this issue again. Moreover, the defendants did not provide laboratory access letters to plaintiffs for any of the films, so the plaintiffs could not have secured prints and pre-print material in order to market the films, 608 F.Supp. at 1365; 684 F.Supp. at 1175, even if copyright protection was available. Therefore, with a few minor exceptions the plaintiffs were unable to sublicense any of these films in West Germany or elsewhere. To the extent that the German copyright evidence could be viewed as tangentially bearing on damages by proving an opportunity to mitigate damages, its exclusion did not substantially affect the outcome.
VII. Sanctions. The district court ordered appellants and their law firm to pay all of the plaintiffs’ attorneys’ fees because the court found an exhibit to be fraudulent and a defense to be unfounded. Exhibit U, the controversial document, would have demolished plaintiffs’ fraud case had it been authentic because it purported to show that the defendants disclosed to Ostano’s assignor, VCI, on April 17, 1980, the limited nature of the defendants’ rights in nine films. Counsel ultimately admitted that he had not turned over Exhibit U to the plaintiffs or listed it in the pretrial order because he was unaware of its existence until Schubert produced it the night before the trial. But throughout the trial and thereafter, counsel cooperated with his client’s effort, Judge Carter found, to “corrupt the court record” by giving the impression that the document had been available to counsel and that he had seen it during the time of document production as well. 608 F.Supp. at 1367-68.
We remand for the district court to decide what proportion of the plaintiffs’ attorney fees resulted from the offensive conduct. Neither of the district court opinions specifically found that all of the plaintiffs’ attorney fees resulted from the merit-less defense and fabricated document, see 608 F.Supp. at 1367-69; 684 F.Supp. at 1177, and this issue was not before us on the first appeal, 794 F.2d at 764. Only those fees attributable to the offensive conduct can be awarded. Sierra Club v. United States Army Corps of Engineers, 776 F.2d 383, 389 (2d Cir.1985) (under bad faith exception to American Rule, fee award limited to expenses necessary to counter losing party’s bad faith), cert. denied, 475 U.S. 1084, 106 S.Ct. 1464, 89 L.Ed.2d 720 (1986); see also Browning Debenture Holders’ Committee v. DASA Corp., 560 F.2d 1078, 1088 (2d Cir.1971).
Judgment modified and, as modified, affirmed, and remanded to the district court for additional findings as to the justification for sanctions and recalculation of prejudgment interest;10 costs to appellees.
. The breach of contract award was for $3,653,-550.91, plus $2,466,816.35 in prejudgment interest.
. The fraud award was for $334,472.66, plus $192,346.42 in prejudgment interest.
. The district court apparently meant $4,914,-000, which is $189,000 times 26.
. Jovy quoted 126,000 DM. The parties appear to accept a 2:1 exchange rate, and we have converted Deutschmark figures to dollar amounts.
. Several clerical errors as to prices appear in the district court’s opinion, see 684 F.Supp. at 1174, but we have consulted the pages in the transcript which the district court cited.
. The court arrived at this number by finding the lowest estimate, from any source, for each of the eight countries, and totaling those numbers to arrive at an estimate for the value of one film’s distribution in eight countries.
. $189,000 is the value of “Blue Gardenia.” The total of the highest estimates from other sources was $187,000.
. The average was actually $3,831,100.
. It is somewhat difficult to tell which defendants are liable for fraud. At the first trial, Telewide and Schubert were both found liable for fraud, and punitive damages were assessed against both. 608 F.Supp. at 1367. We affirmed the holding that both had committed fraud, 794 F.2d at 766, but we requested further consideration of the justification for imposing punitive damages, id. at 768. The most recent district court opinion began by noting our holding that both defendants were liable on the fraud claim for the plaintiffs’ out-of-pocket losses, 684 F.Supp. at 1173, but ended by holding that Schubert was liable for fraud, id. at 1176. The district court did not inform us of its reasons for not imposing liability on Telewide for fraud, although it explained that Schubert's conduct justified assessing punitive damages against him. Given that the district court did not articulate reasons for releasing Telewide from liability for fraud, and given our prior holding that it was liable, we assume that the district court’s failure to award a judgment against Telewide for fraud resulted from a clerical error.
. The district court awarded 9% prejudgment interest on the breach of contract award, calculated from May 13, 1980. 684 F.Supp. at 1176. It awarded prejudgment interest on the fraud award, calculated from Jan. 1, 1985, for $87,-245.43 in principal and from May 13, 1980, for the remainder. Id. at 1176. Because this approach was not appealed, the district court should apply it on remand, using, of course, the revised principal amount for the breach of contract award.