LYNCH, Circuit Judge.

This case raises several novel issues, including an important question of the meaning of the statutory damages provision of the Copyright Act, 17 U.S.C. § 504(c), and the question of whether Fed.R.Civ.P. 59(e) is ever available to alter or amend a default judgment entered under Fed.R.Civ.P. 55(b).

The heirs of a Puerto Rican popular songwriter sued two recording companies for copyright infringement of some of the songwriter's best-selling songs. One of those companies defaulted and ended up with a $1.6 million judgment against it. The judgment was based on statutory damages for sixteen albums that each included at least one of two infringed songs. Plaintiffs also sought actual damages and defendant's profits for a seventeenth album, but the court at the default judgment hearing found that such damages and profits were not proven. The defaulting defendant, Sonolux Records ("Sonolux"), a U.S. company, then moved promptly under Rule 55(c) to set aside the entry of default and the default judgment. Sonolux also moved under Rule 59(e), in the alternative, to amend the judgment to reduce the damages award.

Sonolux's attempt to remove the default and the entry at all of a default judgment was heard and rejected by a second judge. However, that judge granted Sonolux's Rule 59(e) motion to amend the amount of the judgment, and the statutory damages award for the copyright infringement was reduced from $1,600,000 to $200,000 on the ground that the larger amount was based on an incorrect reading of the statutory damages provision of the Copyright Act, 17 U.S.C. § 504(c).

After careful review, we affirm the denial of defendant's motion to set aside the entry of default and the default judgment and affirm the grant of defendant's Rule 59(e) motion. The entry of a default judgment stands, but we vacate the amount of that judgment and remand the amount determination to the district court for further proceedings consistent with this opinion.

I.

Plaintiffs are the children of Guillermo Venegas-Lloveras, a noted composer, who inherited the copyright in 197 of his songs. They filed a copyright infringement suit against Sonolux in U.S. district court in September 2001. Sonolux had published recordings of two of the copyrighted songs, "Desde Que Te Marchaste" and "No Me Digan Cobarde," on sixteen different albums by different artists. Sonolux had also used portions of "Desde Que Te Marchaste" in a seventeenth album called "Sentimientos." Plaintiffs had duly registered their copyright claims to both songs.

Sonolux failed to answer the complaint and a default was entered against it on January 24, 2002, under Fed.R.Civ.P. 55(a). Plaintiffs applied to the court for entry of a default judgment under Fed.R.Civ.P. 55(b)(2) and sent Sonolux notice of the damages hearing. Sonolux still did not appear to defend. Plaintiffs elected to seek statutory damages, rather than to try to prove actual damages and defendant's profits, for sixteen albums. They also sought actual damages for another album called "Sentimientos." Because Sonolux had not appeared, plaintiffs had no opportunity to obtain discovery and thus were disadvantaged in proving actual damages and defendant's profits as to each of the songs.

Plaintiffs represented to the district court that they were entitled to the measure of statutory damages multiplied by the number of albums containing the infringed songs. They did not provide citations, nor did they alert the judge that the statute had been interpreted differently by courts.

On February 3, 2003, the court found that plaintiffs had failed to prove actual damages or profits as to the album "Sentimientos," but, simply accepting plaintiffs' statement of the correct measure of damages, awarded plaintiffs $1.6 million in statutory damages for the infringement of the two songs on the other albums. The court concluded that "an award of $100,000 for each of 16 works, or a total of $1,600,000 represents a fair measure of damages in this case." This was based on "the willful nature of Defendant's conduct as well as the potential to discourage future infringement."

After the default judgment issued on February 19, 2003, Sonolux appeared for the first time on March 6, 2003 and filed a motion under Rule 55(c) to set aside the default entry and default judgment, or, in the alternative, to amend the default judgment under Rule 59(e). In the Rule 59(e) motion, Sonolux argued, inter alia, that the district court had erred in its damages calculation by applying the statutory damages rate to the number of infringing albums (sixteen) rather than to the number of infringed songs (two). The district court, now a different judge, who was the first to address the question of the correct measure of damages, denied Sonolux's motion to set aside the default and default judgment but found the damages calculation to be a "manifest error of law" and granted the Rule 59(e) motion. The court reduced the damages award to $200,000 using the method of statutory damages calculation advanced by Sonolux. This appeal and cross-appeal ensued. Plaintiffs appeal the grant of Sonolux's Rule 59(e) motion to amend the default judgment and the finding that they did not prove defendant's profits on the album "Sentimientos." Sonolux cross-appeals the denial of its motion to set aside the default and default judgment.

II.

Sonolux challenges the denial of its motion to set aside both the entry of default and the entry of a default judgment. Rule 55(c) sets up different standards for setting aside an entry of default under Rule 55(a) and setting aside a default judgment under Rule 55(b). We take up each in turn.

A. The Entry of Default

An entry of the default itself may be set aside "[f]or good cause," Fed.R.Civ.P. 55(c), a term that is liberally construed. United States v. $23,000 in United States Currency, 356 F.3d 157, 164 (1st Cir. 2004). Among the factors that a court may consider are whether the default was willful and whether removal of the default would prejudice the plaintiff. Id. There is no precise formula for the "good cause" analysis. KPS Assoc., Inc. v. Designs by FMC, Inc., 318 F.3d 1, 12 (1st Cir. 2003). Our review of the denial of the motion to set aside the entry of default is for abuse of discretion; we review any factual findings underlying the denial for clear error. Id.

There was no abuse of discretion here. Having been properly served with a summons and a complaint, and later given notice of the damages hearing, defendant intentionally did not appear in the case until more than a year after the filing of the complaint and ten days after the default judgment was entered. Defendant was well aware of the ongoing litigation, and the district court was justified in discounting defendant's excuse. Sonolux claimed that it "never intended to default, reasonably understood that the claims of the Plaintiffs were being properly dealt with, and [was] mistaken in apparently failing to note the significance of the Plaintiffs' filing of a duplicative lawsuit." The court rejected those claims, noting that plaintiffs' suit was a major multi-million dollar copyright infringement action that could not have been easily ignored, that defendant was given proper notice of the suit, and that it was defendant's obligation to learn the specifics of the suit and keep informed of its progress. We believe that the district court did not abuse its discretion in reaching these conclusions. Defendant's decision not to appear also may have prejudiced plaintiffs' case by preventing them from obtaining sufficient evidence on which to prove actual damages and defendant's profits.

B. The Default Judgment

A default judgment may be set aside "in accordance with Rule 60(b)." Fed.R.Civ.P. 55(c). Although Sonolux's motion did not reference Rule 60(b), we understand its argument that the default judgment should be vacated entirely to rely essentially on the theory that its actions in failing to appear constituted "excusable neglect." That argument fits within the requirements of Rule 60(b)(1), which allows a court to relieve a party from a judgment on account of "mistake, inadvertence, surprise, or excusable neglect." The reason for a defendant's delay is a critical factor in the excusable neglect inquiry. See $23,000, 356 F.3d at 164.

Our review of the district court's denial of defendant's Rule 60(b) motion is also for abuse of discretion, id. at 165, and we find none here. For the same reasons that defendant cannot satisfy the more liberal "good cause" standard for setting aside the entry of default, defendant cannot show that its actions constituted "excusable neglect." Defendant has offered no adequate justification for its failure to respond in this case; its decision not to respond appears to have been willful. As a result, the decision that defendant does not deserve a new opportunity to litigate the entry of a default judgment is sound.

III.

Plaintiffs challenge the grant of defendant's Rule 59(e) motion to amend a default judgment by reducing the damages amount. That challenge raises an issue that has not been addressed by either party or previously by this court.

A. Availability of Rule 59(e)

It is by no means clear that a Rule 59(e) motion is even a valid mechanism for altering or amending a default judgment. It is arguable that Rule 55(c) provides the exclusive means for challenging a default judgment through Rule 60(b), which allows relief from a judgment or order. Rule 55(c) states: "For good cause shown the court may set aside an entry of default and, if a judgment by default has been entered, may likewise set it aside in accordance with Rule 60(b)." Rule 60(b), in turn, specifies six grounds for relief. Rule 59(e) provides that "[a]ny motion to amend a judgment shall be filed no later than 10 days after entry of the judgment." Rule 59(e) does not specifically mention default judgments.

In a different context, that of whether a defaulted party had filed a timely notice of appeal, one court of appeals has held that Rule 55(c) (and, by reference, Rule 60(b)) provides the exclusive method for attacking a default judgment. Gulf Coast Fans, Inc. v. Midwest Elec. Imps., Inc., 740 F.2d 1499, 1507 (11th Cir. 1984). In that same context, two other courts of appeals have held that a Rule 59(e) motion is indeed a valid mechanism for attacking a default judgment, in addition to the mechanism of Rule 60(b). United States v. One 1988 Dodge Pickup, 959 F.2d 37, 40 (5th Cir. 1992); Anilina Fabrique de Colorants v. Aakash Chems. Dyestuffs, Inc., 856 F.2d 873, 876 (7th Cir. 1988). This court has noted the issue, but declined to decide it, in a case where the defaulted party's post-judgment motion specifically invoked Rule 55(c) and did not invoke Rule 59(e). Echevarria-Gonzalez v. Gonzalez-Chapel, 849 F.2d 24, 27 (1st Cir. 1988).

Our case presents this issue in a different context. We again decline to resolve it. Plaintiffs have not argued to either this court or the district court that Sonolux could not have used a Rule 59(e) motion at all, and neither party has briefed the issue. As a result, we treat any argument that a Rule 59(e) motion is not a valid mechanism for amending a default judgment as waived.

One might ask why, if there is doubt about the availability of Rule 59(e) to amend a default judgment, we do not just treat the motion to alter the judgment as a Rule 60(b) motion and review it as such. After all, Rule 55, which deals with default judgments, expressly says that such judgments are subject to Rule 60(b) motions.

The answer is that such a solution is foreclosed by circuit precedent in these circumstances. Sonolux's motion to alter the amount of the damages was premised on the argument that a legal error was made as to the statutory measure of damages. Rule 59(e) permits an attack on a judgment on the ground that the judgment is based on a manifest error of law. Bogosian v. Woloohojian Realty Corp., 323 F.3d 55, 72 (1st Cir. 2003); 11 Wright, Miller Kane, Federal Practice and Procedure, § 2810.1 (West 1995). One might, and some courts do, think that Rule 60(b)(1)'s reference to "mistake" as a grounds for relief from judgment includes this type of error of law. But this circuit decided that question the other way in 1971. Silk v. Sandoval, 435 F.2d 1266, 1267-68 (1st Cir. 1971) (Aldrich, C.J.) (a construction of "mistake" under Rule 60(b) that is as extensive as that available under Rule 59(e) undermines the interest in speedy disposition and finality that Rule 59(e) reflects). That may be why Sonolux framed its motion for relief based on error of law as a Rule 59(e) motion.

We have cited Silk favorably since 1971, Ahmed v. Rosenblatt, 118 F.3d 886, 891 (1st Cir. 1997), and it has never been overruled. As one commentator has noted, this circuit's interpretation "seems to fit better the structure of the rules" and "makes more sense of the relation between Rule 59(e) and Rule 60(b)(1)." 11 Federal Practice Procedure, § 2858. However, Silk did not account for the special problem of default judgments.

If Silk is correct about the limited scope of Rule 60(b) and so are the courts that say that Rule 59(e) may not be used to challenge a default judgment, then a party in default would never be able, by motion in the district court, to bring to that court's attention an error of law in the default judgment. Of course, the party could appeal the judgment to the court of appeals, but it would be odd and inefficient to preclude the party in default from first seeking relief based on error of law from the district court. Judge Friendly, taking a different view from Judge Aldrich, made that point in Schildhaus v. Moe, 335 F.2d 529, 531 (2d Cir. 1964) ("[T]here is indeed good sense in permitting the trial court to correct its own error and, if it refuses, in allowing a timely appeal from the refusal; no good purpose is served by requiring the parties to appeal to a higher court, often requiring remand for further trial proceedings, when the trial court is equally able to correct its decision in the light of new authority on application made within the time permitted for appeal . . ."). That particular problem would be exacerbated if, as happened here, the defaulted party also failed to appear at the hearing on the amount of the default judgment. In such circumstances, the defaulting party could never get a hearing before the district court on its argument that the amount embodied in the default judgment is based on an error of law. That might make sense as a strong medicine to encourage parties not to default, but it also could lead to uncorrected basic legal errors. Given this problem, and given that plaintiffs have waived the issue of the availability of the Rule 59(e) motion to defendant in these circumstances, we proceed to plaintiffs' argument that the motion was granted in error.

Plaintiffs do argue that Sonolux should not have been allowed to use the rule to make its particular argument about the meaning of "work" in 17 U.S.C. § 504. They point us to the usual rule that parties cannot use Rule 59(e) motions to raise new arguments that could have been made before judgment issued or to undo their own procedural failures. Bogosian, 323 F.3d at 72; Aybar v. Crispin-Reyes, 118 F.3d 10, 16 (1st Cir. 1997). Rule 59(e) motions are "aimed at re consideration, not initial consideration." F.D.I.C., 978 F.2d at 16 (internal quotation marks omitted and emphasis added); Jorge Rivera Surillo Co., Inc. v. Falconer Glass Indus., Inc., 37 F.3d 25, 29 (1st Cir. 1994). In this way, Rule 59(e) motions allow a court to correct its own errors and avoid unnecessary appellate procedures.

But, assuming arguendo Rule 59(e) can be used for amendment of default judgments, it is an open question whether the usual rule for Rule 59(e) motions — that they cannot be used to raise new arguments — applies where one party is challenging a default judgment and it has not previously appeared. The topic is unaddressed in the case law. The "raise-it-or-waive-it" rule may not always make sense when applied to a default judgment, and does not make sense here, once Rule 59(e) is deemed to apply due to plaintiffs' waiver.

B. Standards of Review

We review for abuse of discretion the district court's decision to grant the Rule 59(e) motion. Williams v. Poulos, 11 F.3d 271, 289 (1st Cir. 1993); DeSenne v. Jamestown Boat Yard, Inc., 968 F.2d 1388, 1392 (1st Cir. 1992). Our abuse of discretion review is superimposed on the standard of review the Rule 59(e) judge exercises over the original judgment. That question is complicated here by the fact that the underlying judgment was a default judgment, not the normal stuff of Rule 59(e) review.

Rule 59(e) itself does not state the grounds on which relief under the rule may be granted, and the district courts have considerable discretion in deciding whether to grant or deny a motion to alter or amend under Rule 59(e). Edward H. Bohlin Co. v. Banning Co., 6 F.3d 350, 355 (5th Cir. 1993); Robinson v. Watts Detective Agency, 685 F.2d 729, 743 (1st Cir. 1982); 11 Wright, Miller Kane, Federal Practice and Procedure, § 2810.1 (West 1995). That discretion requires a balancing of the need for finality of judgments with the need to render a just decision. Edward H. Bohlin Co., 6 F.3d at 355. Under the broad umbrella of the district court's discretionary power, the case law has developed a non-exhaustive list of circumstances in which relief is available under Rule 59(e) that attempts to balance the need for finality with the need for justice. One of those circumstances, articulated in cases where the underlying judgment is not a default judgment, is where the moving party clearly establishes a manifest error of law. F.D.I.C. v. World Univ., Inc., 978 F.2d 10, 16 (1st Cir. 1992). In granting Sonolux's Rule 59(e) motion, the second district judge determined that there was a manifest error of law in the first judge's interpretation of 17 U.S.C. § 504(c). It would be a closer question here if the judgment had entered not by default, but after the parties joined on the issue, whether the error was, indeed "manifest."

In the common case, the judgment being reviewed by the Rule 59(e) judge has been entered after both parties have argued the points at issue. Here, by contrast, the judgment being reviewed was a default judgment and the Rule 59(e) judge was the first to address the legal issues around the question of the statutory measure of damages. Sonolux had never appeared in the case. Finality plays a slightly different role in the default context. This is reflected by the lenient standard for removing entries of default and the only slightly more restrictive standard for setting aside default judgments. We have found no cases discussing the application of the Rule 59(e) standard to a default judgment. Assuming Rule 59(e) is available at all, we think it is clear that the default context is something that a district court can consider in exercising its discretion in order to strike the appropriate balance between finality and justice.

C. Interpretation of 17 U.S.C. § 504(c)

Section 504(c) states that a copyright owner can elect to recover statutory damages "for all infringements involved in the action, with respect to any one work, for which any one infringer is liable individually." The second district judge read that language as meaning "that an infringer's statutory damages liability is based on the number of infringed works" rather than on the number of infringing works.

In support of that interpretation, the district judge pointed to the applicable Report of the Committee on the Judiciary, H.R. Rep. No. 94-1476, at 162 (1976) reprinted in 1976 U.S.C.C.A.N. 5659, 5778, which states: "A single infringer of a single work is liable for a single amount . . . no matter how many acts of infringement are involved in the action and regardless of whether the acts were separate, isolated, or occurred in a related series."

The court also found support for its interpretation in the case law, citing to Walt Disney Co. v. Powell, 897 F.2d 565, 569 (D.C. Cir. 1990) ("Both the text of the Copyright Act and its legislative history make clear that statutory damages are to be calculated according to the number of works infringed, not the number of infringements."), and to a case from this circuit, Gamma Audio Video, Inc. v. Ean-Chea, 11 F.3d 1106, 1116 (1st Cir. 1993). Noting that there were only two infringed works, "Desde Que Te Marchaste" and "No Me Digan Cobarde," the second district judge applied the statutory damages rate set by the first district judge ($100,000 per work) to those two works, resulting in a reduction in the damages award from $1,600,000 to $200,000.

The legal issue of whether under § 504(c) statutory damages are to be applied to each infringed work or to each infringement on a given work is reviewed de novo. A leading commentator, Nimmer, sets up the question as follows:

If in a single action, the same copyrighted work is held to have been infringed by several different infringing acts all committed by the same infringer, does this give rise to only one set of statutory damages, with a statutory minimum of $250 (currently raised to $750) for all such infringing acts, or is the plaintiff entitled to recover at least a minimum of $250, and a separate set of statutory damages, for each such infringing act? The current Act states that only a single minimum, and a single set of statutory damages, will be applicable "for all infringements involved in the action, with respect to any one work, for which any one infringer is liable individually. . . ."

4 M. Nimmer D. Nimmer, Nimmer on Copyright § 14.04[E][2][a] (2001).

Section 504(c) states that a copyright owner may elect "an award of statutory damages for all infringements involved in the action, with respect to any one work, for which any one infringer is liable individually. . . ." Another leading treatise in the field, Goldstein, states without reservation that under § 504(c) statutory damages are available for each infringed work (song), not each act of infringement (album). 2 P. Goldstein, Copyright, § 12.2.2.2(a) (2d ed. 2003 Supp.) ("[A]n infringer will be liable for a single statutory award whether it makes one copy of a copyrighted [work] or one thousand. . . ."). Nimmer comes to a "tentative conclusion" that this reading of the statute, propounded by Goldstein, is correct. 4 Nimmer on Copyright, § 14.04[E][2][c].

The most natural reading of the plain language of the statute is that the song is the "work." There is, though, arguably some ambiguity. The legislative history dissolves any argument of ambiguity:

Although . . . an award of minimum statutory damages may be multiplied if separate works and separately liable infringers are involved in the suit, a single award . . . is to be made "for all infringements involved in the action." A single infringer of a single work is liable for a single amount between $[7]50 and $[3]0,000, no matter how many acts of infringement are involved in the action and regardless of whether the acts were separate, isolated, or occurred in a related series. . . .

. . . . Where the infringements of one work were committed by a single infringer acting individually, a single award of statutory damages would be made.

H.R. Rep. No. 94-1476, at 162, reprinted in 1976 U.S.C.C.A.N. 5659, 5778 (emphasis added).

The one circuit court to have addressed the issue squarely, the D.C. Circuit, has adopted the reading advanced by the second district judge. Walt Disney Co., 897 F.2d at 569 (vacating a damages award that "mistakenly focus[ed] on the number of infringements rather than on the number of works infringed"). Although the precise issue was not presented to the Fifth Circuit, that court addressed it at length in Mason v. Montgomery Data, Inc., 967 F.2d 135 (5th Cir. 1992), as part of its interpretation of 17 U.S.C. § 412, which references § 504. The Fifth Circuit explained:

Under [§ 504(c)(1)], the total number of "awards" of statutory damages . . . that a plaintiff may recover in any given action depends on the number of works that are infringed and the number of individually liable infringers, regardless of the number of infringements of those works. So if a plaintiff proves that one defendant committed five separate infringements of one copyrighted work, that plaintiff is entitled to only one award of statutory damages. . . . And if a plaintiff proves that two different defendants each committed five separate infringements of five different works, the plaintiff is entitled to ten awards, not fifty.

Id. at 143-44 (emphasis in original). The Eleventh Circuit declined to reach the issue in MCA Television Ltd. v. Feltner, 89 F.3d 766 (11th Cir. 1996), because it was not raised before the district court, but the court went on to quote at length from the above section of Mason and also cited Walt Disney. Id. at 770. In Columbia Pictures Television v. Krypton Broadcasting, 106 F.3d 284 (9th Cir. 1997), rev'd on other grounds, Feltner v. Columbia Pictures Tv., 523 U.S. 340, 118 S.Ct. 1279, 140 L.Ed.2d 438 (1998), the Ninth Circuit, citing Mason, stated that "when statutory damages are assessed against one defendant . . . each work infringed may form the basis of only one award, regardless of the number of separate infringements of that work." Id. at 294 (affirming a statutory damages award based on works infringed, where neither party challenged this interpretation of § 504(c)(1)). Language from the Second Circuit's opinion in Twin Peaks Prods., Inc. v. Publ'ns Inter'l, Ltd., 996 F.2d 1366 (2d Cir. 1993), is also consistent with the Walt Disney and Mason interpretations, id. at 1381 ("The current statute shifts the unit of damages inquiry from number of infringements to number of works [infringed]."), but in Twin Peaks there was only one infringing work so the issue was not directly presented.

Our own opinion in Gamma Audio, while not directly on point, implicitly adopts the reading adopted or cited approvingly by those other circuits. In Gamma Audio, we held that the plaintiff was entitled to four awards of statutory damages because the defendant had infringed four separate "works." 11 F.3d at 1118. We observed that the present Copyright Act marked a change in the scheme for awarding statutory damages from the Copyright Act of 1909, and we cited Twin Peaks for the proposition that the current act "shifts the unit of damages inquiry from number of infringements to number of works." Id. at 1116 (quoting Twin Peaks, 996 F.2d at 1381). We also quoted the House Report concerning § 504(c) and cited Walt Disney.

Nimmer cautions that the prevailing reading may lead to adverse results — specifically, game-playing by plaintiffs to separate their various claims of infringements as to any one work into separate lawsuits so as to obtain more than one statutory damages award for each infringed work. Nimmer on Copyright, § 14.04[E][2]. Nimmer does acknowledge that the doctrine of res judicata may act as a curb on this problem, id. at § 14.04[E][2][b]-[c], but he suggests that the law of res judicata might not bar separate suits based on different infringing transactions and that the risk of such game-playing warrants reconsideration of the widely accepted reading of the section, id. at § 14.04[E][2][c].

There are a number of ways in which the problem of game-playing could occur under the prevailing reading and a number of possible solutions to that problem, the discussions of which are beyond the scope of this opinion. And both interpretations of the statute have an accompanying set of potential problems. The current statute represents a departure from the case law interpreting the statute under the earlier Act of 1909. 4 Nimmer on Copyright, § 14.04[E][2][a]; see L.A. Westermann Co. v. Dispatch Printing Co., 249 U.S. 100, 39 S.Ct. 194, 63 L.Ed. 499 (1919) (two separate infringements of the same copyrighted work gave rise to two separate claims for minimum damages). Indeed, problems with the old statute no doubt led to the revision.

The prevailing reading in the circuits is the one that we join: under § 504(c) the total number of "awards" of statutory damages that a plaintiff may recover in any given action against a single defendant depends on the number of works that are infringed and the number of individually liable infringers and is unaffected by the number of infringements of those works. That reading works in the overall context of the statute, flows naturally from the statutory language, and is supported by the legislative history. In re Bankvest Capital Corp., 360 F.3d 291, 299 (1st Cir. 2004). We thus agree with the second district judge that "works" in § 504(c)(1) means "songs" in the context of this case.

D. Application of Abuse of Discretion Standard

That conclusion only brings us back to the initial question of whether the second district judge abused his discretion in granting the Rule 59(e) motion. As already noted, the touchstone of Rule 59(e) relief is limited discretion that honors both the need for finality and the need for justice.

Here, the record provides no reason to think that the first district judge was even aware that there was an issue as to the interpretation of "work" in § 504(c). Had he been aware, we doubt he would have calculated damages as he did. Indeed, no circuit court had ever upheld that method of calculation, and the plain language of the statute reads otherwise. At most, one treatise had suggested, for policy-based reasons, that the statute could be read differently (while another treatise had rejected the suggestion). Given that the issue was never fairly presented to the first district judge, and given the default context in which the original damages award was calculated, the second district judge's decision to grant the Rule 59(e) motion was within the allowable scope of his discretion under the rule. The second judge's determination that Congress's policy choice, reflected in the plain language of § 504(c), should be honored even in the default context of this case seems to us to strike the proper balance between the need for finality of judgments and the need for justice. It was within the district court's province to conclude that amendment of the amount of the damages award was warranted in order to reach a just judgment in accord with congressional intent.

It may seem odd that we would uphold the second judge's determination that the original damages award was in violation of the statute when this Court had never before ruled on the issue. The second district judge, after all, characterized the original damages award as a "manifest error of law." See Black's Law Dictionary 563 (7th ed. 1999) (a manifest error is "[a]n error that is plain and indisputable, and that amounts to a complete disregard of the controlling law."). But for the reasons stated earlier, in the peculiar context of this case, we do not find an abuse of discretion. After all, the situation developed not only because Sonolux defaulted, but also because plaintiffs utterly failed in their obligation to inform the first judge of contrary authority, and should not be rewarded for that lapse.

E. Remedy

Still, we do not simply affirm an award of $200,000 and remand with instructions to enter that judgment. It is quite possible that applying the correct rules, the award should be higher. At the $100,000 per "work" rate set by the original judge, the corrected calculation would automatically produce a reduction in the judgment to $200,000. However, it may be that the first judge would have increased the amount of damages per work, given the number of infringements and given his finding of willfulness, if he had understood that "works" referred to the infringed songs rather than the infringing albums.

The sliding scale for statutory damages is designed in part to allow courts "to increase the amount of the award in proportion to the number of individual infringements." 2 Goldstein, Copyright § 12.2.2.2(a). The sliding scale is also designed to deter willful infringements, and the award can go up to $150,000 per work where willfulness has been found. 17 U.S.C. § 504(c)(2); see H.R. Rep. No. 94-1476, at 162, reprinted in 1976 U.S.C.C.A.N. 5659, 5778 ("The basic principle underlying [§ 504(c)(2)] is that the courts should be given discretion to increase statutory damages in cases of willful infringement and to lower the minimum where the infringer is innocent."); Yurman Design, Inc. v. PAJ, Inc., 262 F.3d 101, 113-14 (2d Cir. 2001) ("[S]tatutory damages are not meant to be merely compensatory or restitutionary. The statutory award is also meant to discourage wrongful conduct. That is why the statute permits consideration of . . . additional damages where an infringement is willful.") (internal citations and quotation marks omitted). Both district judges concluded that the infringements were willful. Indeed, it would be easy to view Sonolux's conduct in this case as demonstrating a continuing disregard for the law. Cf. Morley Music Co. v. Dick Stacey's Plaza Motel, Inc., 725 F.2d 1, 3 (1st Cir. 1983) ("Not only was it a permissible inference that plaintiffs' copyrights were infringed in four prior years but, even if it were not, the other evidence of size of defendants' operation, resistance to production of documents, intent, dissimulation, or at least diffident efforts to exact respect for others' copyrights justified the court's award.").

The first district judge stated that "an award of $100,000 for each of the 16 works, or a total of $1,600,000, represents a fair measure of damages in this case." That language may well mean that the first judge was primarily concerned with the total damages, the $1,600,000, as the sum that would reflect a just award in light of defendant's willfulness and would discourage future infringement. Because the intent of the original order is not clear, we think on remand plaintiffs should be free to argue to the district court that the statutory damages rate should be increased, subject to the statutory cap of $150,000 per song, in light of seventeen infringing works (including the album "Sentimientos") and the willful conduct. The $200,000 award will serve as a damages floor on remand.

Our decision to open this issue on remand is by analogy to criminal law. A decision in an infringement suit to increase the statutory rate based on a finding of willfulness, like an upward departure from a sentencing guideline's range, is a punitive measure meant to deter. Williams v. United States, 503 U.S. 193, 112 S.Ct. 1112, 117 L.Ed.2d 341 (1992), held that a remand is necessary when a district court has used improper factors to justify a sentencing guidelines departure and the appellate court cannot ascertain whether the district court would have imposed the same sentence even if it had not used the improper factors. Id. at 203-204, 112 S.Ct. 1112. That is so because the district court, if apprised of the errors in its interpretation of the Guidelines, may have chosen a different sentence. Id. at 204-05, 112 S.Ct. 1112. Further, we note that in Walt Disney the court of appeals did not itself determine damages, but remanded to the district court without restriction to award appropriate damages. 897 F.2d at 570.

Plaintiffs have not requested the opportunity to have the option of proving actual damages and defendant's profits on remand. As a result, any issue about that option is waived.

This leaves only the plaintiffs' appeal from the conclusion that they did not prove actual damages and defendant's profits on the album "Sentimientos." This aspect of the appeal is largely mooted by our reading of "work" in § 504(c). Under our reading of § 504(c), it is the song, "Desde Que Te Marchaste," to which statutory damages apply and plaintiffs may not seek actual damages for yet another infringing album. The number of infringements is a relevant factor in setting the statutory damages rate, 2 Goldstein, § 12.2.2.2(a), and plaintiffs may argue on remand that the amount of statutory damages should be increased to reflect this seventeenth infringement in the album "Sentimientos."

Of course, the parties are encouraged to attempt to resolve this case on remand by agreement.

IV.

The denial of defendant's motion to set aside the entry of default and the default judgment is affirmed. The grant of defendant's Rule 59(e) motion to amend the default judgment is affirmed insofar as we hold that the original damages calculation was based on a manifest error of law. The amount of the judgment only, and not the entry of the judgment, is vacated, and the case is remanded to the district court for further proceedings consistent with this opinion.