opinion: FRANK MUSIC CORPORATION, Robert Wright, George Forrest, Anne Lederer (as Executrix of the Last Will of Charles Lederer), Luther Davis, and Edwin Lester, Plaintiffs-Appellants-Cross-Appellees, v. METRO-GOLDWYN-MAYER, INC., a Delaware corporation, MGM Grand Hotel, Inc., a Nevada corporation, and Donn Arden, Defendants-Appellees-Cross-Appellants.
  Nos. 83-6426, 83-6460.
  United States Court of Appeals, Ninth Circuit.
  Argued and Submitted Jan. 9, 1985.
  Decided Sept. 23, 1985.
  Reinhardt, Circuit Judge, filed concurring opinion.
  David H. Kornblum, Los Angeles, Cal., for plaintiffs-appellants-cross-appellees.
  Peter F. Sloss, Sloss & Becker, San Francisco, Cal., Frederick F. Greenman, Jr., Linden & Deutsch, New York City, amicus curiae for Songwriters Guild.
  Irwin Karp, New York City, amicus curiae for Dramatists Guild, The Authors League of America.
  Bernard Korman, New York City, Kadi-son, Pfaelzer, Woodard, Quinn & Rossi, John J. Quinn, Howard 0. Boltz, Jr., Los Angeles, Cal., amicus curiae, for American Society of Composers Authors & Publishers.
  Karen Randall, Charles H. Stein, Wy-man, Bautzer, Rothman, Kuchel & Silbert, Los Angeles, Cal., for defendants-appel-lees-cross-appellants.
  Latham & Watkins, Jill S. Slater, John B. Missing, Los Angeles, Cal., Lionel, Sawyer & Collins, Robert D. Faiss, Las Vegas, Nev., amicus curiae for Nevada Resort Assoc.
  Before FLETCHER, BOOCHEVER, and REINHARDT, Circuit Judges.
  FLETCHER, Circuit Judge:
  This copyright infringement suit arises out of defendants’ use of five songs from plaintiffs’ dramatico-musical play Kismet in a musical revue staged at defendant MGM Grand Hotel in 1974-76. After a bench trial, the district court found infringement and awarded the plaintiffs $22,-000 as a share of defendants’ profits. Plaintiffs appeal and defendants cross-appeal. We affirm in part, reverse in part, and remand.
  I. FACTS
  The original version of Kismet was a dramatic play, written by Edward Knob-lock in 1911. Knoblock copyrighted the play as an unpublished work in that year and again as a published work in 1912. Knoblock’s copyright expired in 1967, and the dramatic play Kismet entered the public domain.
  In 1952, plaintiff Edwin Lester acquired the right to produce a musical stage production of the dramatic play Kismet. Lester hired plaintiffs Luther Davis and Charles Lederer to write the libretto and plaintiffs Robert Wright and George Forrest to write the music and lyrics for the musical adaptation. In 1953 and 1954, Led-erer and Davis copyrighted their dramatico-musical play Kismet, and in 1953, Wright and Forrest assigned to plaintiff Frank Music Corporation the right to copyright all portions of the musical score written for Kismet. Frank Music subsequently obtained copyrights for the entire musical score and for each of the songs in the score.
  In 1954, Lederer, Wright, and Forrest entered into a license agreement with Loew’s, Inc., a predecessor of Metro-Goldwyn-Mayer, Inc., (“MGM, Inc.”) granting to it the right to produce a musical motion picture based on plaintiffs’ play. MGM released its motion picture version of Kismet, starring Howard Keel and Ann Blyth, in 1955.
  The story presented in the MGM film and in plaintiffs’ dramatico-musical play is essentially the same as that told in Knob-lock’s dramatic play. It is the tale of a day in the life of a poetic beggar named Hajj and his daughter, Marsinah. The story is set in ancient Baghdad, with major scenes in the streets of Baghdad, the Wazir’s palace, an enchanted garden, and the Wazir’s harem.
  On April 26, 1974, defendant MGM Grand Hotel premiered a musical revue entitled Hallelujah Hollywood in the hotel’s Ziegfield Theatre. The show was staged, produced, and directed by defendant Donn Arden. It featured ten acts of singing, dancing, and variety performances. Of the ten acts, four were labeled as “tributes” to MGM motion pictures of the past, and one was a tribute to the “Ziegfield Follies.” The remaining acts were variety numbers, which included performances by a live tiger, a juggler, and the magicians, Siegfried and Roy.
  The Ziegfield Theatre, where Hallelujah Hollywood was performed, is a lavish showplace. Its special features, including huge elevators used to raise or lower portions of the stage and ceiling lifts capable of lowering performers down into the audience during the shows, reportedly provide impressive special effects.
  Act IV of Hallelujah Hollywood, the subject of this lawsuit, was entitled “Kismet,” and was billed as a tribute to the MGM movie of that name. Comprised of four scenes, it was approximately eleven and one-half minutes in length. It was set in ancient Baghdad, as was plaintiffs’ play, and the characters were called by the same or similar names to those used in plaintiffs’ play. Five songs were taken in whole or in part from plaintiffs’ play. No dialogue was spoken during the act, and, in all, it contained approximately six minutes of music taken directly from plaintiffs’ play.
  The total running time of Hallelujah Hollywood was approximately 100 minutes, except on Saturday nights when two acts were deleted, shortening the show to 75 minutes. The show was performed three times on Saturday evenings, twice on the other evenings of the week.
  On November 1,1974, plaintiffs informed MGM Grand that they considered Hallelujah Hollywood to infringe their rights in Kismet. MGM Grand responded that it believed its use of plaintiffs’ music was covered by its blanket license agreement with the American Society of Composers, Authors and Publishers (“ASCAP”). In 1965, plaintiffs had granted to ASCAP the right to license certain rights in the musical score of their play Kismet.
  Plaintiffs filed this action, alleging copyright infringement, unfair competition, and breach of contract. MGM Grand continued to present Hallelujah Hollywood, including Act IV “Kismet,” until July 16, 1976, when the hotel substituted new music in Act IV. In all, the “Kismet” sequence was used in approximately 1700 performances of the show.
  II. DISCUSSION
  A. Scope of the ASCAP License
  Paragraph one of the ASCAP license gives MGM Grand the right to perform publicly “non-dramatic renditions of the separate musical compositions” in the ASCAP repertory. Paragraph three excludes from the license “dramatico-musical works, or songs [accompanied by] visual representation of the work from which the music is taken____” The district court addressed both of these clauses and concluded that Act IV of Hallelujah Hollywood was nondramatic but contained visual representations of plaintiffs’ play. The court therefore held that Act IV exceeded the scope of the ASCAP license. We review de novo the district court’s interpretation of the agreement because the court interpreted the agreement from the face of the document and as a matter of law. In re Financial Securities Litigation, 729 F.2d 628, 631-32 (9th Cir.1984). We apply the clearly erroneous standard to its findings as to the sufficiency of the visual representations.
  We agree with the result reached by the district court, but not with its approach. We agree that Act IV “Kismet” was accompanied by “visual representation” of plaintiffs’ play. Accordingly, defendants’ use was excluded from the ASCAP license by the express terms of paragraph three. We conclude, however, that there is no reason to consider, as the district court did, whether Act IV was “non-dramatic.”
  The district court found the following “visual representations”: plaintiffs’ songs were performed in Hallelujah Hollywood by singers identified as characters from plaintiffs’ Kismet, dressed in costumes designed to recreate Kismet, and the performance made use of locale, settings, scenery, props, and dance style music of the type used in plaintiffs’ work.
  The defendants do not challenge the finding that their production contained these visual representations. They argue, instead, that the district court failed to give sufficient consideration to whether the visual representations in Act IV were “of the work from which the music is taken,” i.e., plaintiffs’ Kismet. Defendants suggest that this distinction is important because plaintiffs’ Kismet is a derivative work. They argue that many of the visual representations, (e.g., street scenes in ancient Baghdad, swarming bazaars, and an oriental palace), could be said to be derived from Edward Knoblock’s 1911 dramatic version of Kismet rather than from plaintiffs’ Kismet. Since Knobloek’s play is in the public domain, defendants contend these visual representations are not protectable by plaintiffs’ copyright. Defendants further argue that other elements of the “visual representations,” such as choreography style and character names, also are not protectable by copyright.
  We find defendants’ arguments unpersuasive for two reasons. First, their suggestion that they might have derived portions of Act IV from Knoblock’s 1911 play is directly contradicted in the record. Arden created Act IV as a tribute to the MGM musical Kismet, which was derived from plaintiffs’ play. While preparing Act IV, he obtained the Broadway score of plaintiffs’ play and screened the MGM motion picture. The record does not show that any of Act IV was based on Knob-lock’s 1911 dramatic version of Kismet.
  More important, defendants’ argument is unpersuasive because it is simply irrelevant. The question we face is not whether the “visual representations” are copyrightable, but whether the use of a copyrighted work exceeds the scope of an ASCAP license because visual representations accompanied the songs. The license agreement does not refer to “copyrightable” visual representations. The district court was not clearly erroneous in finding that Act IV “Kismet” was accompanied by sufficient visual representations derived from plaintiffs’ play to place the songs’ use beyond the scope of the ASCAP license.
  The district court properly concluded that defendants infringed plaintiffs’ copyrights in Kismet.
  B. Recovery for Infringement
  The Copyright Act of 1909 provided three forms of recovery to a plaintiff whose copyright had been infringed: actual damages, infringer’s profits, or statutory “in lieu” damages. The Act provided for recovery of “such damages as the copyright proprietor may have suffered due to the infringement, as well as all the profits which the infringer shall have made from such an infringement____” 17 U.S.C. § 101(b) (1970). The Act further provided that a court could award “in lieu of actual damages and profits, such damages as to the court shall appear to be just” within certain prescribed minima and maxima. Id.
  A court making an award for copyright infringement must, if possible, determine both the plaintiff’s actual damages and the defendant’s profits derived from the infringement. Sid & Marty Krofft Television Productions, Inc. v. McDonald’s Corp., 562 F.2d 1157, 1172 (9th Cir.1977) (Krofft I). In this circuit, we have construed section 101(b) of the 1909 Act as allowing recovery of the greater of the plaintiff’s damage or the defendant’s profits. Krofft I, 562 F.2d at 1176; Universal Pictures Co. v. Harold Lloyd Corp., 162 F.2d 354, 376 (9th Cir.1947).
  1. Actual Damages
  “Actual damages” are the extent to which the market value of a copyrighted work has been injured or destroyed by an infringement. 3 M. Nimmer, Nimmer on Coyyright § 14.02, at 14-6 (1985). In this circuit, we have stated the test of market value as “what a willing buyer would have been reasonably required to pay to a willing seller for plaintiffs’ work.” Krofft I, 562 F.2d at 1174.
  The district court declined to award actual damages. The court stated that it was “unconvinced that the market value of-plaintiffs’ work was in any way diminished as a result of defendant’s infringement.” We are obliged to sustain this finding unless we conclude it is clearly erroneous. Fed.R.Civ.P. 52(a); see County of Ventura v. Blackburn, 362 F.2d 515, 521 (9th Cir.1966); Shapiro, Bernstein & Co. v. 4636 S. Vermont Ave., Inc., 367 F.2d 236, 241 (9th Cir.1966).
  Plaintiffs contend the district court’s finding is clearly erroneous in light of the evidence they presented concerning the royalties Kismet could have earned in a full Las Vegas production. Plaintiffs did offer evidence of the royalties Kismet had earned in productions around the country. They also introduced opinion testimony, elicited from plaintiff Lester and from Kismet’s leasing agent, that a full production of Kismet could have been licensed in Las Vegas for $7,500 per week. And they introduced other opinion testimony to the effect that Hallelujah Hollywood had destroyed the Las Vegas market for a production of plaintiffs’ Kismet.
  In a copyright action, a trial court is entitled to reject a proffered measure of damages if it is too speculative. See Peter Pan Fabrics, Inc. v. Jobella Fabrics, Inc., 329 F.2d 194, 196-97 (2d Cir.1964). Although uncertainty as to the amount of damages will not preclude recovery, uncertainty as to the fact of damages may. Unviersal Pictures Co. v. Harold Lloyd Corp., 162 F.2d at 369; see also 3 M. Nimmer, supra, § 14.02, at 14-8 to -9. It was the fact of damages that concerned the district court. The court found that plaintiffs “failed to establish any damages attributable to the infringement.” (emphasis in original). This finding is not clearly erroneous.
  Plaintiffs offered no disinterested testimony showing that Hallelujah Hollywood precluded plaintiffs from presenting Kismet at some other hotel in Las Vegas. It is not implausible to conclude, as the court below apparently did, that a production presenting six minutes of music from Kismet, without telling any of the story of the play, would not significantly impair the prospects for presenting a full production of that play. Based on the record presented, the district court was not clearly erroneous in finding that plaintiffs’ theory of damages was uncertain and speculative.
  2. Infringer’s Profits
  As an alternative to actual damages, a prevailing plaintiff in an infringement action is entitled to recover the infringer’s profits to the extent they are attributable to the infringement. 17 U.S.C. § 101(b); Krofft, 562 F.2d at 1172. In establishing the infringer’s profits, the plaintiff is required to prove only the defendant’s sales; the burden then shifts to the defendant to prove the elements of costs to be deducted from sales in arriving at profit. 17 U.S.C. § 101(b). Any doubt as to the computation of costs or profits is to be resolved in favor of the plaintiff. Shapiro, Bernstein & Co. v. Remington Records, Inc., 265 F.2d 263 (2d Cir.1959). If the infringing defendant does not meet its burden of proving costs, the gross figure stands as the defendant’s profits. Russell v. Price, 612 F.2d 1123, 1130-31 (9th Cir.1979), cert. denied, 446 U.S. 952, 100 S.Ct. 2919, 64 L.Ed.2d 809 (1980).
  The district court, following this approach, found that the gross revenue MGM Grand earned from the presentation of Hallelujah Hollywood during the relevant time period was $24,191,690. From that figure, the court deducted direct costs of $18,060,084 and indirect costs (overhead) of $3,641,960, thus arriving at a net profit of $2,489,646.
  Plaintiffs’ challenge these computations on a number of grounds. Several of the objections plaintiffs raise require only brief discussion; we dispose of these in the margin. But three of their objections are more serious, and deserve closer scrutiny. Plaintiffs claim the district court erred in allowing deductions for overhead expenses for two reasons: because the infringement was “conscious and deliberate,” and because defendants failed to show that each item of claimed overhead assisted in the production of the infringement. Plaintiffs also contend the court erred in not including in gross profits some portion of MGM’s earnings on its hotel and gaming operations.
  A portion of an infringer’s overhead properly may be deducted from gross revenues to arrive at profits, at least where the infringement was not willful, conscious, or deliberate. Kamar International, Inc. v. Russ Berrie & Co., 752 F.2d 1326, 1331 (9th Cir.1984); Sammons v. Colonial Press, Inc., 126 F.2d 341, 351 (1st Cir.1942); 3 M. Nimmer, supra, § 14.03[B], at 14-16.1. Plaintiffs argue that the infringement here was conscious and deliberate, but the district court found to the contrary. The court’s finding is not clearly erroneous. Defendants believed their use of Kismet was protected under MGM Grand’s ASCAP license. Although their contention ultimately proved to be wrong, it was not implausible. Defendants reasonably could have believed that their production was not infringing plaintiffs’ copyrights, and, therefore, the district court was not clearly erroneous in finding that their conduct was not willful. See Kamar International, Inc. v. Russ Berrie & Co., 752 F.2d at 1331.
  We find more merit in plaintiffs’ second challenge to the deduction of overhead costs. They argue that defendants failed to show that each item of claimed overhead assisted in the production of the infringement. The evidence defendants introduced at trial segregated overhead expenses into general categories, such as general and administrative costs, sales and advertising, and engineering and maintenance. Defendants then allocated a portion of these costs to the production of Hallelujah Hollywood based on a ratio of the revenues from that production as compared to MGM Grand’s total revenues. The district court adopted this approach.
  We do not disagree with the district court’s acceptance of the defendants’ method of allocation, based on gross revenues. Because a theoretically perfect allocation is impossible, we require only a “reasonably acceptable formula.” Sammons v. Colonial Press, Inc., 126 F.2d at 349; see Kamar International, Inc. v. Russ Berrie & Co., 752 F.2d at 1333. We find, as did the district court, that defendants’ method of allocation is reasonably acceptable.
  We disagree with the district court, however, to the extent it concluded the defendants adequately showed that the claimed overhead expenses actually contributed to the production of Hallelujah Hollywood. Recently, in Kamar International, we stated that a deduction for overhead should be allowed “only when the infringer can demonstrate that [the overhead expense] was of actual assistance in the production, distribution or sale of the infringing product.” 752 F.2d at 1332 (citation omitted); accord Sheldon v. Metro-Goldwyn-Mayer Pictures, Co., 106 F.2d 45, 54 (2d Cir.1939) (Sheldon I), aff'd, 309 U.S. 390, 60 S.Ct. 681, 84 L.Ed. 825 (1940). We do not take this to mean that an infringer must prove his overhead expenses and their relationship to the infringing produc tion in minute detail. See Sheldon I, 106 F.2d at 52; Sterns-Roger Manufacturing Co. v. Ruth, 87 F.2d 35, 41-42 (10th Cir.1936). Nonetheless, the defendant bears the burden of explaining, at least in general terms, how claimed overhead actually contributed to the production of the infringing work. See Kamar International, Inc. v. Russ Berrie & Co., 752 F.2d at 1333; Taylor v. Meirick, 712 F.2d 1112, 1121-22 (7th Cir.1983) (“It is too much to ask a plaintiff who has proved infringement also to do the defendant’s cost accounting.”).
  We do not doubt that some of defendants’ claimed overhead contributed to the production of Hallelujah Hollywood. The difficulty we have, however, is that defendants offered no evidence of what costs were included in general categories such as “general and administrative expenses,” nor did they offer any evidence concerning how these costs contributed to the production of Hallelujah Hollywood. The defendants contend their burden was met when they introduced evidence of their total overhead costs allocated on a reasonable basis. The district court apparently agreed with this approach. That is not the law of this circuit. Under Kamar International, a defendant additionally must show that the categories of overhead actually contributed to sales of the infringing work. 752 F.2d at 1332. We can find no such showing in the record before us. Therefore, we conclude the district court’s finding that “defendants have established that these items of general expense [the general categories of claimed overhead] contributed to the production of ‘Hallelujah Hollywood’ ” was clearly erroneous.
  Plaintiffs next challenge the district court’s failure to consider MGM Grand’s earnings on hotel and gaming operations in arriving at the amount of profits attributable to the infringement. The district court received evidence concerning MGM Grand’s total net profit during the relevant time period, totaling approximately $395,000,-000, but its memorandum decision does not mention these indirect profits and computes recovery based solely on the revenues and profits earned on the production of Hallelujah Hollywood (approximately $24,000,000 and $2,500,000 respectively). We surmise from this that the district court determined plaintiffs were not entitled to recover indirect profits, but we have no hint as to the district court’s reasons.
  Whether a copyright proprietor may recover “indirect profits” is one of first impression in this circuit. We conclude that under the 1909 Act indirect profits may be recovered.
  The 1909 Act provided that a copyright proprietor is entitled to “all the profits which the infringer shall have made from such infringement____” 17 U.S.C. § 101(b). The language of the statute is broad enough to permit recovery of indirect as well as direct profits. See 3 M. Nimmer, supra, § 14.03[A], at 14-15; cf. Nucor Corp. v. Tennessee Forging Steel Service, Inc., 513 F.2d 151, 153 (8th Cir.1975) (common law copyright infringement action; issue of whether infringing use of copyrighted architectural plans resulted in lower manufacturing costs to defendants was properly put to jury). At the same time, a court may deny recovery of a defendant’s profits if they are only remotely or speculatively attributable to the infringement. See 3 M. Nimmer, supra, § 14.03[A]; see, e.g., Roy Export Co. v. Columbia Broadcasting System, Inc., 503 F.Supp. 1137, 1156-57 (S.D.N.Y.1980) (profits from an infringing unsponsored television broadcast could not be ascertained since benefit received by CBS “consists of unmeasurable good-will with affiliates and increased stature and prestige vis-a-vis competitors.”), aff'd, 672 F.2d 1095 (2d Cir.), cert. denied, 459 U.S. 826, 103 S.Ct. 60, 74 L.Ed.2d 63 (1982).
  The allowance of indirect profits was considered in Sid & Marty Krofft Television Productions, Inc. v. McDonald’s Corp., 1983 Copyright L.Rep. (CCH) 1125,-572 at 18,381 (C.D.Cal.1983) (Krofft II), on remand from 562 F.2d 1157 (9th Cir.1977), a case involving facts analogous to those presented here. The plaintiffs, creators of the “H.R. Pufnstuf” children’s television program, alleged that they were entitled to a portion of the profits McDonald’s earned on its food sales as damages for the “Mc-Donaldland” television commercials that infringed plaintiffs’ copyright. The district court rejected as speculative the plaintiffs’ formula for computing profits attributable to the infringement. However, the court’s analysis and award of in lieu damages indicate that it considered indirect profits recoverable. The court stated, in awarding $1,044,000 in statutory damages, that “because a significant portion of defendants’ profits made from the infringement are not ascertainable, a higher award of [statutory] in lieu damages is warranted.” Id. at 18,-384; see also Cream Records Inc. v. Jos. Schlitz Brewing Co., 754 F.2d 826, 828-29 (9th Cir.1985) (discussed supra note 7) (awarding profits from the sale of malt liquor for Schlitz’s infringing use of plaintiff’s song in television commercial).
  Like the television commercials in Krofft II, Hallelujah Hollywood had promotional value. Defendants maintain that they endeavor to earn profits on all their operations and that Hallelujah Hollywood was a profit center. However, that fact does not detract from the promotional purposes of the show — to draw people to the hotel and the gaming tables. MGM’s 1976 annual report states that “[t]he hotel and gaming operations of the MGM Grand — Las Vegas continue to be materially enhanced by the popularity of the hotel’s entertainment[, including] ‘Hallelujah Hollywood’, the spectacularly successful production revue____” Given the promotional nature of Hallelujah Hollywood, we conclude indirect profits from the hotel and gaming operations, as well as direct profits from the show itself, are recoverable if ascertainable.
  3. Apportionment of Profits
  How to apportion profits between the infringers and the plaintiffs is a complex issue in this case. Apportionment of direct profits from the production as well as indirect profits from the hotel and casino operations are involved here, although the district court addressed only the former at the first trial.
  When an infringer’s profits are attributable to factors in addition to use of plaintiff’s work, an apportionment of profits is proper. Sheldon v. Metro-Goldwyn Pictures, Inc., 309 U.S. 390, 405-06, 60 S.Ct. 681, 686-87, 84 L.Ed. 825 (1939) (Sheldon II); Universal Pictures Co. v. Harold Lloyd Corp., 162 F.2d at 377. The burden of proving apportionment, (i.e., the contribution to profits of elements other than the infringed property), is the defendant’s. Lottie Joplin Thomas Trust v. Crown Publishers, Inc., 592 F.2d 651, 657 (2d Cir.1978). We will not reverse a district court’s findings regardmg_^porti.QQment unless they are clearly erroneous. See Shapiro, Bernstein & Co. v. 4636 S. Vermont Ave., Inc., 367 F.2d at 241-42.
  After finding that the net profit earned by Hallelujah Hollywood-jazz approximately $2,500,000, the-distr-ie-t-eourt-offered the following explanation_of apportionment:
  While no precise mathematical formula can be applied, the court concludes in light of the evidence presented at trial approximation of £ho profits-o£-Act IV attributable to the infringement is $22,-000.
  The disfcw«t-conrt was correct that mathematical exactnesses not required. However, a reasonable and just apportionment of profits is required. Sheldon II, 309 U.S. at 408, 60 S.Ct. at 688; Universal Pictures Co. v. Harold Lloyd Corp., 162 F.2d at 377.
  Arriving at a proper method of apportionment and determining a specific amount to award is largely a factual exercise. Defendants understandably argue that the facts support~tEeUfísWtet-eourt’s award. They claim that the infringing material, six minutes of music in Act IV, was an unimportant part of the whole show, that the unique features of the Ziegfield Theater contributed_mo_K§_jx> the show’s success than any other factor. This is proved, they argue, bifTEe" fact that when the music from Kismet was removed from Hallelujah Hollywood in 1976, the show suffered no decline in attendance and the hotel received no complaints.
  Other evidence contradicts defendants’ position. For instance, defendant Donn Arden testified that Kismet was “a very_im-portant part of the show” and “[he] hated to see it go.” Moreover, while other acts were deleted from the shortenecLSaturday night versions of the show, Act IV “Kismet” never was.
  We reject defendants’ contention that the relative unimportance of the Kismet music was proved by its omission and the show’s continued success thereafter. Hallelujah Hollywood was a revue, comprised of many different entertainment elements. Each element contributed significantly to the show’s success, but no one element was the sole or overriding reason for that success. Just because efie element could be omitted and the show goes oñctoes not prove that the elemeni was noTimportant in the first instance ami did~not contribute to establishing the show’s initial popularity.
  The difficulty in this case is that the district court has not provided_us with any reasoned explanation of. or formularor its apportionment. We know only the district court’s bottom line: that the plaintiffs are entitled to $22,000. Given the nature of the infringement, the character of the infringed property, the success of defendants’ show, and the magnitude of the defendants’ profits, the amount seems to be grossly inadequate. It amounts to less than one percent of MGM Grand’s profits from the show, or roughly $13 for each of the 1700 infringing performances.
  On remand, the district court should reconsider its apportionment of profits, and should fully explain on the record its reasons and the resulting method of apportionment it uses. Apportionment of indirect profits may be a part of the calculus. If the court finds that a reasonable, nonspecu-lative formula cannot be derived, or that the amount of profits a reasonable formula yields is insufficient to serve the purposes underlying the statute, then the court should award statutory damages. See infra Part II.B.5.
  4. Liability of Joint Infringers
  The district court granted judgment of $22,000 “against defendants” in the plural. Yet if the district court intended that each of the defendants be jointly and severally liable for the $22,000 award, this was error.
  When a copyright is infringed, all infringers are jointly and severally liable for plaintiffs’ actual damages, but each defendant is severally liable, for his or its own illegal profit', one defendant is not liable for the profit — made—by—another. MCA, Inc. v. Wilson, 677 F.2d 180 186 (2d Cir.1981); 3 M. Nimmer, supra, § 12.-04[C][3], at 12-50; see Cream Records, Inc. v. Jos. Schlitz Brewing Co., 754 F.2d at 829.
  The rule of several liability for profits applies, at least, where defendants do not act as partners, or_((pradically — partners.’ Compare Belford, Clarke & Co. v. Scribner, 144 U.S. 488, 507-508, 12 S.Ct. 734, 740, 36 L.Ed. 514 (1892) (printerjield-joint-ly liable for publisher’s pref-its--©n — infringing book since they were “practically partners.”), with Sammons v. Colonial Press, Inc., 126 F.2d at 346-47 (court refused to hold printer jointly liable for publisher’s profits since printer was paid a fixed price for work, payable whether or not infringing books made profit). Defendants assert that Arden and MGM Grand are jointly liable since they “worked closely together” in producing the infringing work. This is a fact question for the district court to consider on remand. The court should consider whether Arden was an employee or an independent contractor rather than a partner. Relevant to this determination, among others, are such factors as whether Arden received a fixed salary or a percentage of profits and whether he bore any of the risk of loss on the production.
  Arden mav be liable for profits he earned in connection.wifh the pmdiTFF.Thri of Haltelujah Hollywood, but amounts paid to hini. as- salar-y-am not_taZph considered as profits. See MCA, Inc. v. Wilson, 677 F.2d at 186. But if Arden did earn profits from the productioñT~§uch as royalties, lie j¡sJiableYdr~a proportionate^ amount of these,- -Goncomita]itLy,-defendant MGM Grand-would-be-entitled-ta.,deduct any such royalties as costs in arriving at its own profits. See Smith v. Little, Brown & Co. 396 F.2d 150, 151-52 (2d Cir.1968; see Cream Records, Inc. v. Jos Schlitz Brewing Co., 754 F.2d at 829 (interpreting the 1976 Act).
  The court must also determine whether MGM, Inc., MGM Grand’s parent corporation, should be held liable for the infringement. A parent corporation cannot be held liable for the infringing actions of its subsidiary unless there is a substantial and continuing connection between the two with respect to the infringing acts. 3 M. Nimmer, supra, § 12.04[A], at 12-44 to -45.
  If the district court finds a “substantial and continuing connection” between MGM Grand and MGM, Inc., then MGM, Inc., may also be liable for its profits. But to the extent any such profits are merely passed on from its subsidiary, MGM Grand, the plaintiffs should be given only one recovery, to be satisfied by either MGM, Inc. or MGM Grand.
  5. Statutory “In Lieu” Damages
  Statutory damages are intended as a substitute for profits or actual damage. When injury is proved but neither the infringer’s profits nor the copyright holder’s actual damages can be ascertained, an award of statutory “in lieu” damages is mandatory. Russell v. Price, 612 F.2d at 1131-32; Pye v. Mitchell, 574 F.2d 476, 481 (9th Cir.1978); Sid & Marty Krofft Television Productions, Inc. v. McDonald’s Corp., 562 F.2d 1157, 1178-79 (9th Cir.1977) (Krofft I). But if either profits or actual damages or both can be ascertained, the trial court has discretion to award statutory damages. Krofft I, 562 F.2d at 1178. Such an award must be in excess of the amount that would have been awarded as profits or actual damages. Id. We review a district court’s award or refusal to award statutory damages for abuse of discretion. Russell v. Price, 612 F.2d at 1132.
  A determination as to whether to award statutory damages must abide the district court’s reconsideration of whether to award damages based on profits. On remand, the district court should keep in mind the purposes underlying the remedy provisions of the Copyright Act, i.e., to provide adequate compensation to the copyright holder and to discourage wrongful conduct and deter infringements. See F.W. Woolworth Co. v. Contemporary Arts, Inc., 344 U.S. 228, 233, 73 S.Ct. 222, 225, 97 L.Ed. 276 (1952); Kamar International, Inc. v. Russ Berrie & Co., 752 F.2d at 1332; Russell v. Price, 612 F.2d at 1131. Thus, in determining whether to exercise its discretion to award statutory damages, the district court must consider whether the amount of profits that have been proved accomplish the purposes of the statute. If not, it should exercise its discretion to award statutory “in lieu” damages that do effectuate the statutory purposes.
  The $22,000 awarded by the district court obviously is too little to discourage wrongful conduct or to deter infringement.
  6. Attorneys’Fees
  The plaintiffs requested that the district court award attorneys’ fees under 17 U.S.C. § 116 (1970). The court omitted mention of plaintiffs’ request in its memorandum decision, although during the course of the proceedings, it had noted that the issue was before it. On remand, the district court can address this issue.
  C. Plaintiffs’ Other Claims
  In addition to claims for copyright infringement, plaintiffs pleaded claims for unfair competition and breach of contract. The district court rejected both of these ancillary claims. We affirm.
  1. Unfair Competition
  To prevail on a claim of unfair competition, a plaintiff must demonstrate a likelihood of confusion. Walt Disney Productions v. The Air Pirates, 581 F.2d 751, 760 (9th Cir.1978), cert. denied, 439 U.S. 1132, 99 S.Ct. 1054, 59 L.Ed.2d 94 (1979); Alpha Industries, Inc. v. Alpha Steel Tube & Shapes, Inc., 616 F.2d 440, 443 (9th Cir.1980). Any findings of fact underlying a determination as to likelihood of confusion are subject to the clearly erroneous test, but determination of whether, based on those facts, a likelihood of confusion exists is a legal conclusion. Alpha Industries, 616 F.2d at 443-44; J.B. Williams Co., Inc. v. Le Conte Cosmetics, Inc., 523 F.2d 187, 190 (9th Cir.1975), cert. denied, 424 U.S. 913, 96 S.Ct. 1110, 47 L.Ed.2d 317 (1976).
  Plaintiffs attempted to prove unfair competition by showing that the title “Kismet” had acquired secondary meaning referring to their play. The only evidence offered by plaintiffs on this issue was the testimony of plaintiff Edwin Lester who claimed that the original 1911 Kismet was a “dead issue.” Defendants introduced evidence that the 1911 Kismet and a silent movie produced from that play in 1912 had been very popular and widely acclaimed. The trial court’s finding that the title “Kismet” had not acquired secondary meaning referring to plaintiff’s play, is not clearly erroneous. Moreover, since Act IV “Kismet” was only an 11-minute segment of a 100-minute revue, we agree that audiences were not likely to confuse the two versions.
  2. Breach of Contract
  Finally, plaintiffs urge that the district court denied them due process in dismissing their breach of contract claim against MGM, Inc. The court indicated at the outset of trial that it would not exercise pendent jurisdiction and would not receive evidence on the contract claim or the unfair competition claim. But at the end of the trial, the court permitted post-trial briefs, specifying that they should include issues relating to plaintiffs’ pendent claims. The court stated it would take additional evidence on those claims if necessary. Since plaintiffs apparently did not offer any additional evidence, the district court did not err in dismissing the contract claim based on the evidence before it. Accordingly, plaintiffs’ due process challenge has no merit.
  III. CONCLUSION
  We affirm the district court’s finding that defendants’ use of plaintiffs’ Kismet exceeded the scope of the ASCAP license. We also affirm the district court’s finding that plaintiffs failed to prove actual damages. We vacate the award of defendants’ profits derived from the infringement and remand to the district court for further proceedings consistent with this opinion.
  AFFIRMED in part, REVERSED in part, and REMANDED with directions.
  . Paragraph one provides:
  Society grants and Licensee accepts for a period commencing as of January 1, 1974 and ending December 31, 1978 a license to perform publicly by means of live entertainment or mechanical music (as defined in paragraph 2), and by no other means, at or in any part of section of the hotel or motel known as MGM Grand Hotel, 3645 Las Vegas Blvd. So., Las Vegas, Nv. 29109 non-dramatic renditions of the separate musical compositions copyrighted or composed by members of Society and of which Society shall have the right to license the performing rights.
  . Paragraph three provides:
  This license shall not extend to or be deemed to include: (a) Oratories, choral, operatic or dramatico-musical works (including plays with music, revues and ballets) in their entirety, or songs or other excerpts from operas or musical plays accompanied either by words, pantomime, dance, or visual representation of the work from which the music is taken; but fragments of instrumental selections from such works may be instrumentally rendered without words, dialogue, costume, accompanying dramatic action or scenic accessory, and unaccompanied by any stage action or visual representation (by motion picture or otherwise) of the work of which such music forms a part, (b) Any work (or part thereof) whereof the stage presentation and singing rights are reserved.
  . Whether some visual representations, less significant than those presented here (e.g., performance of the same five songs as those performed here by a single character dressed in ancient Arabian costume), would be enough to take a performance out of the ASCAP license is a more difficult question, which we need not resolve.
  . Applicable here since the actions complained of all occurred prior to January 1, 1978. See Copyright Revision Act of 1976, Pub.L. No. 94-533, § 112, 90 Stat. 2541, 2600; Kamar International, Inc. v. Russ Berrie & Co., 752 F.2d 1326, 1329 (9th Cir.1984). The citations to the Copyright Act contained in this opinion are to the 1909 Act, unless otherwise indicated.
  . Other circuits disagree with our interpretation of the 1909 Act and allow recovery of both actual damages and the infringer’s profits. See, e.g., Miller v. Universal City Studios, Inc., 650 F.2d 1365, 1376 (5th Cir.1981); Lottie Joplin Thomas Trust v. Crown Publishers, Inc., 456 F.Supp. 531 (S.D.N.Y.1977), aff'd, 592 F.2d 651 (2d Cir.1978). Under the current Copyright Act, 17 U.S.C. § 504 (1982), a prevailing plaintiff is entitled to recover both actual damages and the infringer’s profits. See Transgo, Inc. v. Ajac Transmission Parts Corp., 768 F.2d 1001, 1023 (9th Cir.1985); 3 M. Nimmer, Nimmer on Copyright § 14.01[A] (1985).
  . Plaintiffs additionally argue that we should review the district court’s findings de novo because, they contend, the court erred in applying the actual damages test set forth in Sid & Marty Krofft Television Productions, Inc. v. McDonald’s Corp., 562 F.2d 1157 (9th Cir.1977).
  The district court stated the test as “what a willing buyer would have been reasonably willing to pay to a willing seller for plaintiff’s work,” (emphasis added), rather than “what a willing buyer would have been reasonably required to pay” for the property, Id. at 1174 (emphasis added). This distinction is important, plaintiffs contend, because when an infringement destroys any potential market for the copyrighted work, it becomes impossible to determine what a willing buyer would have been "reasonably willing” to pay; there simply is no willing buyer left.
  Plaintiffs misconstrue the test stated by the district court and misconceive the nature of the Krofft test itself. The test is not what some buyer was willing to pay, but what a buyer would have been willing to pay for a use of a plaintiff’s work similar to the defendant’s use. In other words, the Krofft test seeks to approximate what a reasonable market price would have been at the time of the infringement, not afterwards. The trial court's statement of the Krofft test takes into account the essence of that test. Any misstatement is trivial, and is not error. Therefore, we review the district court’s findings as to damages under the clearly erroneous test.
  . Another panel of this court considered a similar problem recently in Cream Records, Inc. v. Jos. Schlitz Brewing Co., 754 F.2d 826 (9th Cir.1985) (interpreting the 1976 Act). In Cream Records, the jury found that Schlitz and its advertising agency infringed Cream’s copyright in "The Theme from Shaft”, by using a ten-note ostinato from the song in a television commercial. The district court awarded $12,000 as actual damages for loss of licensing fees. We concluded that the award was insufficient, stating:
  The only evidence before the court was that unauthorized use of the Shaft theme music in Schlitz’s commercial ended Cream’s opportunity to license the music for this purpose. There was no evidence that Schlitz sought, or Cream was willing to grant, a license for use of less than the entire copyrighted work, that a license limited to the portion used in the commercial would have had less value, or that use limited to this portion would have had a less devastating effect upon Cream’s opportunity to license to another. Since defendants’ unauthorized use destroyed the value of the copyrighted work for this purpose, plaintiff was entitled to recover that value as damages.
  Id. at 827-28 (citation omitted).
  In Cream Records, the evidence showed that another advertiser had approached Cream for a license for the song, but withdrew when the Schlitz commercial was aired. "There was testimony that use of a well-known popular song in a commercial destroys its value to other advertisers for that purpose.” Id. at 827.
  The evidence concerning the effect of defendants’ infringement is far less convincing in our case. Plaintiffs did introduce testimony that the infringement had destroyed the Las Vegas market for a full production of Kismet, but that testimony came from Kismet's leasing agent, not a disinterested party. We agree with the district court’s characterization of this evidence as "meager," and we cannot conclude that the court clearly erred in discrediting it.
  . Plaintiffs raise several other arguments concerning actual damages, which require only brief discussion.
  Plaintiffs argue that the trial court should have accepted their evidence because the defendants did not offer contrary evidence. But a trier of fact may properly reject uncontradicted testimony so long as it does so with good reason. NLRB v. Klaue, 523 F.2d 410, 414 (9th Cir.1975). Such evidence properly may be rejected because of its inherent unbelieveability, because a witness's demeanor raises doubt as to his sincerity, or because the testimony is clouded with uncertainty. Woods v. United States, 724 F.2d 1444, 1452 (9th Cir.1984); Lewis & Taylor, Inc. v. Commissioner, 447 F.2d 1074, 1077 (9th Cir.1971).
  Plaintiffs suggest that actual damages to the Las Vegas market should be presumed, that such damages are the “natural and probable result” of an unauthorized performance. Yet, plaintiffs rely for this conclusion on cases in which trial courts found damages merely as a matter of fact, see, e.g., Metrto-Goldwyn-Mayer, Inc. v. Showcase Atlanta Cooperative Productions, Inc., 479 F.Supp. 351 (N.D.Ga.1979), or presumed irreparable injury for purposes of issuance of preliminary injunctions, see, e.g., Uneeda Doll Co. v. Regent Baby Products Corp., 355 F.Supp. 438, 445 (E.D.N.Y.1972). These cases do not suggest, as plaintiffs apparently contend, that a copyright owner is relieved from or aided in proving actual damages by some presumption. See Shapiro, Bernstein & Co. v. 4636 S. Vermont Ave., Inc., 367 F.2d 236, 241 (9th Cir. 1966) (plaintiff in copyright action who failed to produce evidence of damages could not complain when trial court determined that no damages were proved).
  Plaintiffs further argue that the court accorded so little weight to plaintiff Edwin Lester’s testimony concerning the value of Kismet as to be tantamount to excluding it. While Universal Pictures Corp. v. Harold Lloyd Corp., 162 F.2d 354, 369 (9th Cir.1947), held that a copyright owner may testify as to the value of his property, that case did not hold that a court may not consider the self-serving nature of such testimony. See Range v. Lee, 441 F.2d 579, 582 (9th Cir.) ("Credible testimony by the owner of literary property regarding its value can provide an adequate evidentiary basis for an award of damages.” (emphasis added)), cert. denied, 404 U.S. 887, 92 S.Ct. 197, 30 L.Ed.2d 169 (1971). The district court was entitled to give Mr. Lester’s testimony slight weight.
  Finally, plaintiffs contend the district court improperly excluded as irrelevant evidence of royalties other Broadway shows had earned in Las Vegas productions. The exclusion was not error. See Universal Pictures Corp. v. Harold Lloyd Corp., 162 F.2d at 372, 374-75 (action for violation of motion picture copyright; not error to exclude evidence of value of another movie as not relevant to value of movie involved).
  . Plaintiffs argue that the trial court should have granted their motion to exclude evidence of costs as a sanction for failure to cooperate in discovery. Fed.R.Civ.P. 37(d). The trial court denied plaintiffs’ motion on the grounds that both parties had been dilatory in pursuing discovery, and that the plaintiffs could not show that they suffered any prejudice as a result of defendants’ alleged failures. A district court has wide discretion in controlling discovery and its rulings will not be disturbed absent a clear abuse of discretion. See Reygo Pacific Corp. v. Johnston Pump Co., 680 F.2d 647, 649 (9th Cir. 1982). We find no abuse here.
  Plaintiffs next argue that the district court should have excluded an exhibit prepared by MGM Grand to show an allocation of costs and expenses to its production of Hallelujah Hollywood. They contend the underlying records from which the summary was prepared were never provided to plaintiffs for inspection, as required by Fed.R.Evid. 1006. But the trial court, after a full hearing on this issue, concluded the underlying records had been made available to plaintiffs. Indeed, plaintiffs’ counsel stated, "I was satisfied with the financial documents that they made available.” The requirements for Rule 1006 are met when the trial judge ascertains that the underlying documents are made available for inspection, City of Phoenix v. Com/Systems, Inc., 706 F.2d 1033, 1038 (9th Cir.1983), and this is so even if opposing counsel fails to avail himself of the opportunity to review the documents. United States v. Denton, 556 F.2d 811, 816 (6th Cir.), cert. denied, 434 U.S. 892, 98 S.Ct. 269, 54 L.Ed.2d 178 (1977). The district court did not abuse its discretion in admitting defendants’ exhibit.
  Plaintiffs also challenge admission of defendants’ summary of costs on the ground that it was "self-calculated” and “unverified.” Rule 1006 does not contemplate that summaries must be prepared by someone independent of the party offering the summary. Plaintiffs had ample opportunity to cross-examine MGM Grand’s Vice-President of Finance, under whose direction the summary was prepared. Any inaccuracies in the cost estimates could have been brought out on this cross-examination. The district court did not abuse its discretion. See Frank Horton & Co. v. Cook Electric Co., 356 F.2d 485, 492 (7th Cir.), cert. denied, 384 U.S. 952, 86 S.Ct. 1572, 16 L.Ed.2d 548 (1966).
  Finally, plaintiffs contend that any evidence of MGM Grand’s indirect costs was inadmissible since such evidence was not mentioned in the pretrial conference order. Fed.R.Civ.P. 16. Aside from the fact that it is arguable whether the language of the order omits mention of this evidence, the issue was litigated at trial and thus the pretrial order may be deemed to have been amended by the consent of the parties. See Simpson Timber Co. v. Palmberg Construction Co., 377 F.2d 380, 386 (9th Cir.1967); Perfection Cobey Co. v. City Tank Corp., 597 F.2d 419, 420 (4th Cir.1979).
  . With one exception, the court accepted the defendant's cost calculations in their entirety. The exception was that defendants had amortized preproduction costs for Hallelujah Hollywood over the first three years of the show’s run, totalling $3,166,000 for the period in question. The district court concluded, instead, that preproduction costs should be amortized over the full six and one-half year run of the show, making the total $1,461,000 for the relevant period.
  . The apportionment percentages in similar cases are markedly higher. See, e.g., Universal Pictures Co. v. Harold Lloyd Corp., 162 F.2d at 377 (infringing use of one comedv-sketch in motion picture; court affirmed award of 20% of infringing movie’s profits); MCA, Inc. v. Wilson, 677 F.2d 180, 181-82 (2d.Cir.1981) (defendants copied substantial portion plaintiffs song, "Boogie Woogie Bugle Bov” — substituted “dirty’’ lvrics, and performed the song as a portion of an erotic nude show; court affirmed special master’s award of approximately $244,000 representing 5% of defendants’ total profits from the show); Lottie Joplin Thomas Trust v. Crown Publishers, Inc., 592 F.2d at 657 (fttfringing songs filled one side of five-record set; court affirmed award of 50% of profits because inclusion of infringing songs made record set the only “complete” collection of Scott Joplin's works); Abkco Music, Inc. v. Harrisongs Music, Ltd., 508 F.Supp. 798, 800-801 (S.D.N.Y.1981) (infringing song reproduced on one side of single record, "flip side” contained noninfringing song, court awarded 70% of profits from sales of the single because infringing song was more popular than noninfringing song; similarly, court awarded 50% of profits for reproduction of same song on album containing twenty-one other songs).
  . Plaintiffs contend that the district court did not impose any award against defendants MGM, Inc. and Donn Arden, and therefore an award of statutory damages is mandatory. We do not resolve this issue because, as we noted above, see supra Part II.B.4, it is not clear which parties the district court intended to be held liable.
  We note, however, that plaintiffs’ argument presents an unresolved issue: How the Krofft rule applies in the context of multiple infring-ers, when actual damages cannot be proved and profits of some, but not all, infringers can be proved.