One of the challenging socio-legal questions raised by this copyright infringement case involves the extent to which the buyers of men’s “sophisticate” magazines are motivated to purchase a particular magazine by the cover photo. The question is no less difficult when the photo is, as it is here, one of Raquel Welch in the buff (modestly covering herself in the nature of September Morn). The United States District Court for the Southern District of New York, Robert W. Sweet, Judge, in assessing damages against the publishers of “Superstars of Celebrity Skin, Special No. 6” (“Celebrity Skin”), thought, and hence found, that the photo — retouched from its original appearance in “Paris Match” — produced 75% of the magazine’s sales. Judge Sweet declared the figure of 75% appropriate “based on the nature of the Photograph, the reputation and fame of Ms. Welch, the absence of any established readership for the publication and its intermittent publication schedule.” Restrained as we are now by amended Rule 52(a), Fed.R.Civ.P., we nevertheless believe the finding of 75% must be modified because it *91is clearly erroneous. We also make some other modifications on the basis of the evidence and the record so as to reduce the judgment in amount while affirming the responsibility of all the named defendants for the judgment.
The Raquel Welch photo in question was taken in 1978 by one Tony Kent, who assigned the copyright to Playboy Enterprises. Playboy Enterprises, in accordance with a contract which it had earlier entered into with Ms. Welch and Raquel Welch Productions, Inc., then assigned her corporation the copyright. The photo subsequently appeared on the cover of the September 4, 1981, issue of “Paris Match” magazine with the title “ ‘Je veux étre la plus belle grand-mére du monde,’ Les secrets d’un corps parfait, á 42 ans.” On May 31, 1983, Raquel Welch Productions, Inc., assigned the copyright on the photo to Sygma Photo News, Inc., appellee here. All the assignments were duly registered with the copyright office.
A retouched version of the photograph— one that understandably omitted references to “Paris Match” and to Ms. Welch’s professed desire to be the world’s most beautiful grandmother — was subsequently used as the cover of the magazine “Celebrity Skin” without authorization. The cover logo refers to the “Superstars of Celebrity Skin in the Nude” and mentions the names not only of Raquel Welch but of other famous women such as Farrah Fawcett, Morgan Fairchild, Jodie Foster, Linda Evans, inevitably Marilyn Monroe, Sophia Loren, Nastassja Kinski, Angie Dickinson, Ursula Andress, Valerie Perrine, “And All Your All-Time Favorites!” The cover also contained a subhead “The Definitive Collector’s Edition from High Society, Special No. 6.”
“Celebrity Skin” was published in the name of Dorjam Publications, Inc., which has no paid employees and is a shell corporation of Drake Publishers. Drake, the successor in interest to High Society Magazine, Inc., which terminated its business in 1979, publishes “High Society,” a monthly men’s sophisticate magazine. According to the deposition testimony of Ira Kirschenbaum, who is Dorjam’s nominal vice president as well as the vice president and CEO of Drake Publishers, Drake administered the publication of “Celebrity Skin” on behalf of Dorjam and Celebrity Skin. Drake’s employees gathered the photographs used in the magazine, kept the books, wrote all the checks, prepared the print order for “Celebrity Skin, Special No. 6,” filed Dorjam’s tax returns, and performed other administrative tasks.
The district court, 596 F.Supp. 28, awarded summary judgment against Dorjam and Drake as infringers of the copyright of the photograph. The parties then avoided a damages trial by stipulating to the facts necessary for the court to determine damages. Noting that once gross revenues from the infringing work were established the burden rested upon the infringer to prove those expenses that should be deducted to establish profit, see Lottie Joplin Thomas Trust v. Crown Publishers, Inc., 592 F.2d 651, 657 (2d Cir.1978), Judge Sweet made an award of $59,283 under section 504(b) of the Copyright Act of 1976, 17 U.S.C. § 504(b) (1982), for actual damages. In calculating expenses, the court decided that all printing, laminating, wrapping and binding costs, a total of $165,070, should be deducted. On a cross-appeal Sygma claims that only 52% of that amount is properly deductible because only that percentage of copies printed were sold. Sygma also urges that the infringer should not be permitted to deduct any expenses related to the photograph and that the district court should not have deducted $42,-882, the entire cost of separations, a procedure whereby color is broken down for printing purposes into separate films, each in a basic color. Drake Publishers and Dorjam Publications maintain on appeal that the chain of title to the photograph was unclear and that the district court therefore erred in granting summary judgment against Dorjam. They also contend that there was insufficient evidence to support a determination on summary judgment that Drake was a contributory infringer. Finally, they argue that, if they are found *92guilty of infringement, then damages should be recalculated. They claim that certain expenses not allowed by the district court, such as those for retouching, were properly deductible. In particular, they maintain that the district court determination that 75% of the magazine’s profits were attributable to Ms. Welch’s photograph was clearly erroneous.
We have little trouble upholding the summary judgment against both Drake and Dorjam. Appellants contend that the grant of summary judgment was inappropriate because there was insufficient evidence to rebut their assertion that Sygma either never had a valid copyright or that the copyright was forfeited by virtue of the French publication. The evidence before the district court, however, shows that plaintiff is entitled to bring this suit for infringement of its copyright. An unchallenged affidavit showed that Tony Kent was the photographer who had executed an assignment to Playboy. The line of copyright assignment after the picture was taken is clear in the record; there is nothing to indicate that Sygma fraudulently procured its copyright registration, or that the photograph might have been published without a copyright notice. Moreover, under 17 U.S.C. § 410(c) (1982) a certificate of copyright registration procured within five years after first publication of the work is prima facie evidence of the validity of a copyright and of the facts stated in the certificate. That presumption of validity and of compliance with all formalities applies to an assignee, such as Sygma, who makes the first registration of a claim of statutory copyright in his name. 3 M. Nimmer, Nimmer on Copyright § 12.11[C], at 12-80, 81 (1985). Appellants therefore bear the burden of proof, and they have failed to satisfy it. The record thus clearly established that Dorjam had infringed on a valid copyright.
That Drake is guilty of infringement is equally clear. All persons and corporations who participate in, exercise control over, or benefit from the infringement are jointly and severally liable as copyright infringers. See, e.g., Shapiro, Bernstein & Co. v. H.L. Green Co., 316 F.2d 304, 308-09 (2d Cir.1963); 3 M. Nimmer, Nimmer on Copyright § 12.04[A], at 12-34 (1985). At the very least, Drake exercised control over the infringement: Drake employees, Drake capital, and Drake labor produced “Celebrity Skin.” Cf. Ann-Margaret v. High Society Magazine, Inc., 498 F.Supp. 401 (S.D.N.Y.1980) (court states that High Society Magazine, Inc., the predecessor in interest of Drake, and Dorjam published “High Society Celebrity Skin”). That a shell corporation was the nominal publisher of the magazine is irrelevant. Infringers may not shield themselves from liability by dummy corporations such as Dorjam, see Shapiro, Bernstein, 316 F.2d at 308-09.
We come then to the damages. We reject Sygma’s claim that the total printing cost allocable to the 48% of the copies that went unsold, i.e., $79,234, should not be deducted. All the expert witnesses, including Sygma’s witness Ronald Scott; a magazine publishing consultant, testified that it is necessary in the skin magazine business to print approximately twice as many copies as will be sold in order to obtain proper distribution. Indeed, if a publisher cuts his print order to match anticipated sales, he will succeed only in reducing his sales by the same percentage as the percentage cut in the print order. Since issues not sold are ultimately destroyed, the entire printing expense is a cost of doing business. The cases relied upon by Sygma disallowing the deduction for unsold copies involved books and lithographic prints that remained unsold but were held in inventory and intended for sale, Smith v. Little, Brown & Co., 273 F.Supp. 870, 874 (S.D.N. Y.1967), aff'd, 396 F.2d 150 (2d Cir.1968); Alfred Bell & Co. v. Catalda Fine Arts, Inc., 86 F.Supp. 399, 413 (S.D.N.Y.1949), modified, 191 F.2d 99 (2d Cir.1951). In the present case, the parties stipulated that the unsold issues of Celebrity Skin were not placed in inventory, but were instead destroyed. The costs for the unsold 48% were properly deducted. See Sheldon v. *93Metro-Goldwyn Pictures Corp., 106 F.2d 45, 54 (2d Cir.1939), aff'd, 309 U.S. 390, 60 S.Ct. 681, 84 L.Ed. 825 (1940) (allowing a deduction for wasted pictures as a necessary incident to profits received on the infringing pictures).
We also think that the district court, 603 F.Supp. 829, properly allowed the entire $42,882 spent on “separations.” Of this amount, $1,280 was attributable to the cost of readying the cover photo for publication. A similar amount, however, would have to have been spent to prepare any cover photo for reproduction. Thus, the $1,280 was not a cost associated with the infringement. It was instead a properly deductible business expense, like the rest of the $42,882 spent on separations.
The district court erred, however, in disallowing in their entirety the retouching expenses of $20,266 for the entire magazine. Expenses incurred in order to make an infringement more difficult to discover — as opposed to those that the infringer incurs in altering an original for some other purpose but that have the incidental effect of concealing — are not reasonable expenses and are therefore not deductible. Judge Sweet apparently found that appellants retouched the background of the “Paris Match” photograph in order to defeat Sygma’s rights. The record indicates that this is a finding to which it is appropriate to defer. It was therefore proper to disallow some percentage of retouching expenses. In disallowing all such expenses, the district court asserted that there was no way of determining exactly what portion of the $20,266 was attributable to retouching the Raquel Welch photo since the parties had stipulated that it was impossible to give a precise amount. The stipulation also said, however, that a Drake-Dorjam executive would testify if he were called that “based upon available records, retouching applicable to the Raquel Welch cover includes $1,950.00 paid to Acorn Communications, and that other invoices indicate that additional sums were allocable to retouching the Raquel Welch cover but it is impossible based upon defendants’ records to give a precise amount.” The judge was correct in concluding that defendants did not prove the allocation with precision. Yet some allocation should be made since the cost of retouching the infringing photo surely did not equal the total retouching costs. On balance, we allow a retouching cost deduction of 80%, i.e., $16,212.
Dorjam and Drake also challenge the district court’s determination that none of the $22,873 paid by Dorjam for photographs used in the issue was deductible. Judge Sweet concluded that the infringers had offered inadequate evidence linking the cost of the photographs to the cost of producing the issue in question. He noted that they had merely stated that in general 50-75% of the photographs originally purchased for an issue were actually used in the particular issue, rather than in a later one, and failed to provide evidence of what the photographs actually used in “Celebrity Skin, Special No. 6” cost. Once again, Judge Sweet was correct in concluding that defendants had not proven the exact amount of their expenses. Defendants, however, should be allowed to deduct an amount equivalent to the minimum amount they in all likelihood spent on the issue. $11,436.50, 50% of the amount spent on photographs, represents such a figure.
The district court did permit the deduction of $2,377 in payments to Drake for type, stats, art supplies and royalties, although it denied any deduction for depreciation, rent, or legal fees under Aitken, Hazen, Hoffman, Miller, P.C. v. Empire Construction Co., 542 F.Supp. 252, 264 (D.Neb.1982). Judge Sweet’s decision was correct in both instances. The link between the former expenses and the production of the issue was established. The latter expenses were not linked with production costs in any satisfactory form; there was not even, as there had been with the photographs, any suggestion of a minimum amount that must have been spent on the issue’s production.
*94Gross revenues for Dorjam were $340,-661. In addition to the $237,977.50 in deductible expenditures discussed above, there were $51,288 in expenses for salaries, editorial costs, freight, transportation, and other miscellaneous expenditures that both sides agreed should be deducted from revenue. Dorjam’s profit was therefore $51,-395.50.
The critical element in determining damages concerns the proper allocation of profit to the infringing photo. The parties stipulated that the expert testimony regarding the importance of cover photos in the case of Childers v. High Society Magazine, Inc., No. 82 Civ. 1905 (S.D.N.Y.), presented before Magistrate Gershon, should be considered as the expert testimony in this case. The parties also recognized, however, that the court could take into account the differences between “High Society” and “Celebrity Skin, Special No. 6.” Thus, the court could consider the fact that “High Society” had been published on a regular monthly basis since 1975 and contained feature articles, letters to the editor, jokes, cartoons, advertising, and an occasional giveaway item such as a record, poster, or 3D glasses, while “Celebrity Skin” was not regularly published and did not have these features.
One of the defense’s experts in Childers was Albert Getson, the president of Kable News Company, a national distributor of books and magazines. He testified that the typical man looking to buy a men’s magazine decides which one to buy by going to the men’s section of the magazine rack and “pulling out magazines to see which one he wants.” Getson opined that it would not make much difference to this “impulse buyer” whether there was a female celebrity on the cover. He did not name any numerical percentage of sales attributable to the cover.
Another defense expert, Dr. Charles Winick, a psychologist in private practice and a professor of sociology at the City University of New York graduate school who had done consumer studies for the President’s Commission on Obscenity and Pornography in 1969, also declared that the cover is relatively unimportant. He testified that the typical purchaser of a men’s magazine is a male who has in advance a reasonable knowledge of the likely contents of the magazine. He knows what will be in the magazine because he is by and large a repeat purchaser; he is “brand loyal” and thus predisposed to purchase a given magazine. The purchaser’s knowledge extends to the range of contents, the degree of explicitness, the quality of the photographs, the nature of the text, and any special qualities that are connected with the magazine. The purchase is normally made in a convenience store, drug store, airport stationery section, or at a newsstand, and the purchaser often does not look at the magazine both because the packaging often makes it difficult to leaf through periodicals of this type and because many people are embarrassed to be seen spending time with such magazines. Dr. Winick testified that for the ten or so years of its life “High Society” has featured celebrities, actresses, and other people in the public eye. He disagreed completely with the theory that men’s magazines are in general purchased impulsively in an emotional response to the cover. Dr. Winick said that the most common purchase decision is “the exact opposite of an upsurging, spontaneous emotional decision.” It is his view that the great majority of the people who buy “High Society” do so because of the brand name rather than because of who particularly is on the cover.
Jeffrey Goodman, also called as a witness for the defendant before Magistrate Gershon, was at the time of his appearance editor and publisher of the magazine “Oui.” The aspect of his testimony of greatest relevance to this case concerned an issue of “High Society” that in approximately half the country featured a cover photograph of Jodie Foster but in the other half used as its cover photograph a picture of a model who was a noncelebrity. According to Goodman, the two versions were within a couple of percentage points of each other in terms of sales. While his *95testimony suggested that the cover photograph has relatively little effect on sales, he did not attempt to estimate what percentage of people purchased the magazine because of the cover.
Ronald Scott, the plaintiffs sole witness, testified that purchases of men’s magazines are most commonly the product of a four-step process of impulse buying. Scott’s testimony on this point followed that which he had earlier given in the case of Playboy Enterprises, Inc. v. Chuckleberry Publishing, Inc., 486 F.Supp. 414 (S.D.N.Y.1980). Scott’s description, to use the Chuckleberry court’s summary, ran as follows:
[C]overs are designed to attract a consumer’s attention. The consumer looks first at the subject on the cover, then to the cover lines, and then, in the case of a sex-oriented magazine, to the center or centerfold if one exists. The decision to buy or not is then made as an emotional response, usually in a matter of seconds.
486 F.Supp. at 427. In addition, in his appearance before Magistrate Gershon, Scott stated that 10 to 25% of the buyers of “High Society” make that purchase because they like the cover photograph.
The result that Magistrate, Gershon, drawing on this expert testimony, reached in the Childers case is illuminating. Noting that the percentage of profits produced by the cover photo could not be determined with precision, she correctly held that want of precision is not a ground for denying apportionment altogether. Childers v. High Society Magazine, No. 82 Civ. 1905 (S.D.N.Y. May 31, 1985) (Report and Recommendation) at 19-20. Confronted with imprecision in the computation of expenses, the court should err on the side of guaranteeing the plaintiff a full recovery. See MCA, Inc. v. Wilson, 677 F.2d 180, 186 (2d Cir.1981); Orgel v. Clark Boardman Co., 301 F.2d 119, 121-22 (2d Cir.), cert. denied, 371 U.S. 817, 83 S.Ct. 31, 9 L.Ed.2d 58 (1962); Sheldon, 106 F.2d at 48-51. Taking into account all of the evidence, she found that the infringing photographs could be fairly treated as responsible for 20% of the “High Society” defendants’ profits. Childers, Report and Recommendation at 19. She declined to award the 25% mentioned by Scott because the relative sales performance of the infringing issues did not justify the assumption that the infringing cover photos should be treated as if they had produced sales at the highest end of the range of percentage sales associated with cover photographs. Magistrate Gershon’s methodology and resulting determination are convincing. Id. at 20. Judge Sweet nevertheless concluded, based upon the same testimony, that “75% of the sales [of “Celebrity Skin”] were attributable to the Photograph [of Ms. Welch].”
Before the 1985 amendment to Fed.R. Civ.P. 52(a), we held that that rule did not require the appellate court to apply the “clearly erroneous” test where the trial court’s findings did not rest on demeanor evidence or evaluation of a witness’s credibility but rather were based upon a purely documentary record, e.g., Taylor v. Lombard, 606 F.2d 371, 372 (2d Cir.1979), cert. denied, 445 U.S. 946, 100 S.Ct. 1346, 63 L.Ed.2d 781 (1980). The Advisory Committee on Rules, however, has declared that considerations turning on the nature of the evidence were “outweighed by the public interest in the stability and judicial economy that would be promoted by recognizing that the trial court, not the appellate tribunal, should be the finder of the facts.” See Fed.R.Civ.P. 52 advisory committee note. The Advisory Committee continued, “To permit courts of appeals to share more actively in the fact-finding function would tend to undermine the legitimacy of the district courts in the eyes of litigants, multiply appeals by encouraging appellate retrial of some factual issues, and needlessly reallocate judicial authority.” Id. Thus the 1985 amendment states that findings of fact, whether based upon oral or documentary evidence, shall not be set aside “unless clearly erroneous”; the amendment adopts the view of Professor Wright, The Doubtful Omniscience of Appellate Courts, 41 Minn.L.Rev. 751, 769-70 (1957), and returns to the views of the original draftsman of *96Rule 52, Charles E. Clark (later Chief Judge of this court), as set forth in 5A J. Moore & J. Lucas, Moore’s Federal Practice ¶ 52.04 at 52-107 n. 15 (2d ed. 1985).
Having the rule clearly in mind, we nevertheless think that the district court’s finding of an allocation of 75% must be overturned. That finding is clearly erroneous. This is true not iust becansellt is radically inconsistent with the expert testimony in the case. That testimony can be discounted to a certain-ex-tent-beeause-líCe?, lebrity Skin” has a different publishing format and schedule from that of its monthly sister “High Society.” Plainly the court could reasonably think that a certain additional percentage of sales would be attributable to the cover on an occasional magathe cover of “Celebrity Skin” noted the connection with “High Society” magazine in its reference to the collector’s edition. More significant, the district court did not make reference to or give_any weight to the fact that thereover ltselfTin addition to’’ containing the photograph of Raquel Welch, referred to the numerous other celebrities of not inconsiderable fame whose nude photos were contained within the magazine. True, decisions in matters such as these are to some extent ad hoc, cf. Soptra Fabrics Corp. v. Stafford Knitting Mills, Inc., 490 F.2d 1092, 1093 (2d Cir. 1974) (quoting Peter Pan Fabrics, Inc. v. Martin Weiner Corp., 274 F.2d 487, 489 (2d Cir.1960) (Hand, J.)), which may leave a certain room for subjective exercises of judgment. But while the district court concededly was influenced by the photograph of Ms. Welch, referring to it as both “infringed, and impressive,” it gave in our opinion too much weight to the impulse nature of a purchase of this sort and to Scott’s testimony. In our view the highest percentage of sales and hence profits attributable to the cover photograph in this case which the district court could reasonably and correctly have awarded would be 50%. We therefore find that damages are $25,697.75, which is 50% of $51,395.50, the amount of profits.
The judgment is affirmed to the extent indicated herein, and the cause is remanded to the district court for entry of a modified judgment revised as to damages in conformity with this opinion; costs to neither party.