SUMMARY ORDER
Defendants-appellants Lai Ying Music and Video Trading, Inc. and Wei Ping Yuan appeal the May 25, 2005, 2005 WL 1231645, judgment of the United States District Court for the Southern District of New York (Cote, /.), granting summary judgment for plaintiff U2 Home Entertainment, Inc. (“U2”) on its claims of copyright infringement, awarding U2 $7,050,000 in damages, and ordering defendants to pay U2 $300,000 as a civil contempt fine. Defendants also appeal the district court’s September 12, 2005, 2005 WL 2230454, order denying defendants’ motion to amend, modify, or withdraw the judgment pursuant to Rule 59 of the Federal Rules of Civil Procedure. We assume the parties’ familiarity with the facts, procedural history, and specification of issues on appeal.
Defendants argue that the district court erred in granting summary judgment and then awarding maximum statutory damages based on a finding of willful infringement. We review a district court’s summary judgment ruling de novo. See Blanch v. Koons, 467 F.3d 244, 249 (2d Cir.2006). We review the district court’s determination that defendants willfully infringed U2’s copyright for clear error, see Hamil Am. Inc. v. GFI, 193 F.3d 92, 97 (2d Cir.1999), and we review the court’s award of damages for abuse of discretion, see Nihon Keizai Shimbun, Inc. v. Comline Bus. Data, Inc., 166 F.3d 65, 74 (2d Cir.1999). We affirm the summary judgment ruling and the award of damages for substantially the same reasons set forth in the district court’s opinion. Although defendants now attempt to point to defects in the title documents supporting U2’s claim of copyright ownership, defendants raised only general objections to these documents before the district court. Thus, defendants’ specific claims of defect are waived, because they were raised for the first time on appeal. See Allianz Ins. Co. v. Lerner, 416 F.3d 109, 114 (2d Cir.2005).
Defendants also argue that the district court improperly calculated the civil contempt fine levied with respect to two of the forty-nine films at issue. We review a contempt order for abuse of discretion. See OSRecovery, Inc. v. One Groupe Int’l, Inc., 462 F.3d 87, 93 (2d Cir.2006). However, “because the power of a district court to impose contempt liability is carefully limited, our review of a contempt order for abuse of discretion is more rigorous than would be the case in other situations in which abuse-of-discretion review is conducted.” Id. (internal quotation marks omitted). In contrast to the punitive nature of a criminal contempt order, a civil contempt order is remedial in nature. Id. at 92 n. 2. A civil contempt fine may be coercive or compensatory. Paramedics Electromedicina Comercial, Ltda v. GE Med. Sys. Info. Techs., Inc., 369 F.3d 645, 657 (2d Cir.2004). Where a fine serves a coercive purpose, a “court has broad discretion to design a remedy that will bring *30about compliance.” Id. (internal quotation marks omitted). On the other hand, where a fíne is compensatory, “the district court has less discretion.” Id. at 658. Unlike a coercive fíne, a compensatory fine is payable directly to the opposing party. As a result, “the sanction should correspond at least to some degree with the amount of damages.” Id. (emphasis added) (internal quotation marks omitted). While a fine may be both coercive and compensatory, “some proof of loss must be present to justify its compensatory aspects.” Id. (emphasis added) (quoting N.Y. State Nat’l Org. for Women v. Terry, 886 F.2d 1339, 1353 (2d Cir.1989)).
In this case, the record indicates that the challenged award was intended to be compensatory and not coercive. The district court ordered defendants to pay a contempt fine “to compensate the plaintiff for the losses suffered due to the infringing conduct and the associated harm to its business reputation.” In calculating the award, the court explained that “[i]n the absence of access to the defendants’ business records it is difficult to calibrate the sanction to the damages suffered from the contemptuous conduct.” Therefore, the court concluded that it was “appropriate to apply the statutory formula for damages as a reasonable proxy” for compensatory damages. We recognize that defendants’ failure to participate adequately in discovery made it very difficult for the district court to calculate the appropriate fine. Such conduct should hardly inure to their benefit. See RSO Records, Inc. v. Peri, 596 F.Supp. 849, 862 (S.D.N.Y.1984) (“Any information which may be available on the exact amount of profits or damages is entirely in the hands of the defendants .... They have chosen to remain silent. Plaintiffs should not be penalized thereby.”). However, while some approximation may be necessary, we emphasize that the “sanction should correspond at least to some degree with the amount of damages.” Paramedics Electromedicina Comercial, Ltda, 369 F.3d at 658 (internal quotation marks omitted). We do not foreclose the possibility that in some civil contempt cases, statutory damages may be useful in estimating actual damages. See, e.g., Time Warner Cable of N.Y. City v. U.S. Cable T.V., Inc., 920 F.Supp. 321, 329 (E.D.N.Y.1996). But in this case, the district court erred in imposing civil contempt sanctions equivalent to the maximum statutory damages for “willful” copyright violations under 17 U.S.C. § 504(c)(2) because such damages are punitive in nature, see On Davis v. The Gap, Inc., 246 F.3d 152, 172 (2d Cir.2001), and thus inconsistent with the remedial purpose of a compensatory civil contempt fine. In sum, the district court abused its discretion when it ordered defendants to pay a civil contempt fine that was implicitly based not only on compensating plaintiffs reasonably estimated loss but also on punishing defendants’ willfulness. Accordingly, we vacate and remand for further proceedings following discovery with respect to the compensatory fine as to two of the forty-nine films at issue. Should defendants not participate adequately in such discovery, the district court may, after further submissions from U2, conclude that the fine it initially imposed continues to be its best estimate of “proof of loss” under the circumstances, so long as the basis for the district court’s conclusion is not the statutory damages figure for “willful” infringement.
We have considered defendants’ remaining arguments and find them to be without merit. For the reasons set forth above, the judgment of the District Court is hereby AFFIRMED in part and VACATED AND REMANDED in part.