SNEED, Circuit Judge:

Cooling Systems and Flexibles, Inc. appeals the dismissal of its copyright infringement action, pursuant to Fed.R. Civ.P. 41(b), at the close of its presentation of evidence. It alleges that the district court erred in several respects: (1) by holding that a typographical error in its copyright registration certificate prevented its radiator catalog from receiving a valid registration; (2) by holding that the Manufacturing Clause, 17 U.S.C. § 601 (1982), denied copyright protection to its catalog; (3) by holding that it omitted any notice of copyright from more than a few copies of its catalog, thus dedicating the material in that catalog to the public domain; (4) by holding that no substantial similarity existed between its catalog and the Stuart Radiator catalog; (5) by refusing to admit into evidence a second version of the allegedly infringing Stuart Radiator catalog, published and distributed after commencement of the case; and (6) by awarding attorneys' fees to Stuart Radiator without making a finding that the claim for infringement was frivolous or in bad faith. Both parties seek attorneys' fees on appeal. We affirm the district court's judgment.

I. [2] FACTS AND PROCEEDINGS BELOW

Appellant Cooling Systems and Flexibles, Inc. (Cooling Systems) is a California corporation that sells replacement radiators for small and imported cars. In March 1981, it published a new edition of its illustrated radiator catalog and distributed the catalog to warehouse parts distributors and independent radiator repair shops. Appellee Stuart Radiator, Inc. (Stuart), is a California corporation that manufactures and sells radiator cores. In June 1981, Stuart published and distributed its first illustrated radiator catalog.

In March 1982, Cooling Systems filed a complaint in federal district court alleging that Stuart had infringed its copyright in the 1981 catalog. The district court dismissed the complaint for failure to state a claim. We reversed the dismissal, which we treated as a summary judgment, on the ground that Cooling Systems had raised triable issues of fact with respect to the issues of infringement and damages. See Cooling Systems Flexibles, Inc. v. Stuart Radiator, Inc., 711 F.2d 1062 (9th Cir. 1983) (mem.).

On remand, the district court dismissed the action after Cooling Systems presented its case.

II. [6] DISCUSSION

A. Standards of Review.

Findings of fact made by a judge after a bench trial are subject to the "clearly erroneous" standard of review, Wilson v. United States, 645 F.2d 728, 730 (9th Cir. 1981), even when those findings are composed of wholesale adoption of proposed findings submitted by counsel. Anderson v. City of Bessemer City, ___ U.S. ___, 105 S.Ct. 1504, 1511, 84 L.Ed.2d 518 (1985). Findings on the issue of "substantial similarity" of expression, in particular, are findings of fact, and therefore are reviewable under the "clearly erroneous" standard. See Twentieth Century-Fox Film Corp. v. MCA, Inc., 715 F.2d 1327, 1328 n. 2 (9th Cir. 1983); Sid Marty Krofft Television Productions, Inc. v. McDonald's Corp., 562 F.2d 1157, 1166 (9th Cir. 1977); International Luggage Registry v. Avery Products Corp., 541 F.2d 830, 831 (9th Cir. 1976). Awards of attorneys' fees in copyright claims are reviewed under an "abuse of discretion" standard. Harris v. Emus Records Corp., 734 F.2d 1329, 1335 (9th Cir. 1984); Russell v. Price, 612 F.2d 1123, 1132 (9th Cir.), cert. denied, Drebin v. Russell, 446 U.S. 952, 100 S.Ct. 2919, 64 L.Ed.2d 809 (1980).

B. The Typographical Error in the Registration Certificate Was Harmless.

17 U.S.C. § 411(a) (1982) states that "no action for infringement of the copyright in any work shall be instituted until registration of the copyright claim has been made in accordance with this title." At trial, the district court noticed that Cooling Systems had registered Catalog 1-4 instead of the allegedly infringed Catalog 1-5. E.R. at 456. Rejecting Cooling Systems' argument that the error was merely typographical, and disregarding its claim that it had sent a correction to the Copyright Office, the court found that "[Cooling Systems] did not register a copyright on [Catalog 1-5] prior to commencing this action." E.R. at 28.

This finding is inconsistent with 17 U.S.C. § 408(d) (1982). Absent fraud, "a misstatement or clerical error in the registration application . . . will not invalidate the copyright nor render the registration certificate incapable of supporting an infringement action." 2 M. Nimmer, Nimmer on Copyright § 7.20, at 7-147 (1985) [hereinafter cited as Nimmer]; see Harris v. Emus Records Corp., 734 F.2d 1329, 1335 (9th Cir. 1984); Original Appalachian Artwork, Inc. v. Toy Loft, Inc., 684 F.2d 821, 828 (11th Cir. 1982); Baldwin Cooke Co. v. Keith Clark, Inc., 383 F. Supp. 650, 655 (N.D.Ill.), aff'd, 505 F.2d 1250 (7th Cir. 1974), and supplemented by 420 F. Supp. 404 (N.D.Ill. 1976).

Moreover, Stuart was not prejudiced by the typographical error in the registration certificate. Cooling Systems corrected the mistake by filing a supplementary application with the Copyright Office, detailing the change in the catalog's volume number. At trial, Cooling Systems attempted to introduce evidence of mailing the supplemental application and of including the requisite fees. E.R. at 63-64. Whether Cooling Systems' offer of proof of mailing included a proof of receipt by the Copyright Office is unclear. In any event, the district court should have admitted the evidence concerning the supplemental registration, even if the proof of receipt evidence was missing. Its failure to do so was error. Nonetheless, it was harmless. A remand would serve no useful purpose. The parties litigated the infringement issue as if catalog 1-5, and not catalog 1-4, possessed the copyright. See Cancellier v. Federated Department Stores, 672 F.2d 1312, 1316 (9th Cir.) (error affecting substantial rights of a party is grounds for reversal unless it was not prejudicial), cert. denied, 459 U.S. 859, 103 S.Ct. 131, 74 L.Ed.2d 113 (1982); see also Ommaya v. National Institute of Health, 726 F.2d 827, 830 (D.C.Cir. 1984).

C. The Error in Interpretation of the Manufacturing Clause Was Harmless.

Cooling Systems next argues that the district court erred by holding that the Manufacturing Clause, 17 U.S.C. § 601(a) (1982), denied copyright protection to its catalog. 17 U.S.C. § 601(a) prohibits, in certain specified instances, "the importation into or public distribution in the United States of copies of a work consisting preponderantly of nondramatic literary material that is in the English language . . . unless the portions consisting of such material have been manufactured in the United States or Canada." The district court erred by holding that the Manufacturing Clause denied copyright protection to Cooling Systems' catalog. Section 601(d) does not invalidate protection for a work under this title; it merely gives an alleged infringer "a complete defense" with respect to all of "the nondramatic literary material comprised in [the] work." See 2 Nimmer, § 7.22[C][3], at 7-162. This error is immaterial because of a larger, but also immaterial, error of the district court. The larger error is that the Manufacturing Clause is not available to Stuart Radiator in any event.

In its application of the Manufacturing Clause, the district court found that the catalog was printed in Singapore, that it was a "work made for hire" as defined by § 601 of the Copyright Act, and that it was "prepared for" Cooling Systems in California, as defined by the Manufacturing Clause. E.R. at 28. Section 601(b)(1) provides that the Manufacturing Clause does not apply where the author of a "substantial part" of an imported work is "neither a national nor a domiciliary of the United States." In the case of a "work made for hire," this "foreign author" exemption is available whenever "a substantial part of the work was prepared for an employer or other person who is not a national or domiciliary of the United States or a domestic corporation or enterprise." Thus, the nationality of the author of a "work made for hire" is that of the employer-corporation and not that of the individual employee-writer. 2 Nimmer, § 7.22[A][4], at 7-157. Cooling Systems sought to use the foreign author exemption on the ground that Cooling Systems Flexibles (PTE) Ltd. (Cooling Systems Singapore), which produced the catalog, was the "foreign author."

The district court rejected this view. As it saw it, the words "prepared for," as used in section 601(b)(1), refer to the nationality or domicile of the employer that actually uses the work, which in this case was Cooling Systems in California. Because Cooling Systems in California is a "domestic corporation," the foreign author exemption was unavailable. E.R. at 103.

Although the issue is not free from doubt, we believe that the words "prepared for" mean only that an employee created the work in the course of employment for his employer. The House Report on the Copyright Act of 1976 strongly suggests that "prepared for" a foreign corporation means that a work is created by an employee, in the course and scope of his employment, for a foreign employer-corporation. See H.R.Rep. No. 1476, 94th Cong., 2d Sess. 167 reprinted in 1976 U.S.Code Cong. Ad.News 5659, 5783. We, therefore, must reject the district court's contrary view.

Nonetheless, the error is harmless. Although not denied protection of the copyright laws by the Manufacturing Clause, Cooling Systems fails on other grounds.

D. Cooling Systems' Omission of Notice Dedicated the Arrangement of the Catalog to the Public Domain.

Cooling Systems based Catalog 1-5 on two earlier catalogs, 1-3 (published in 1979) and 1-4 (published in 1980). Brief for Appellant at 27. Although Catalog 1-5 "contains approximately 30% more models" than Catalog 1-4, the facts in 1-5 "are arranged, with minor variations, in the same manner as in the underlying catalogs." Id. At trial, Stuart, introducing a copy of the 1979 catalog that did not have a copyright notice, argued that the material in the catalog had been dedicated to the public domain and that therefore all of the 1979 material incorporated in the 1981 catalog was not protected by copyright.

Cooling Systems' response was first, that Stuart's introduction of a single catalog without a copyright notice did not meet the burden of proving that Cooling Systems had omitted the notice from more than a relatively few copies and, second, that the certificate of copyright registration in the 1981 catalog — being a copyright in a derivative work — preserved Cooling Systems' right to sue for infringement of both the new and underlying works. We reject both arguments.

Turning to the burden of proof contention, we commence by observing that 17 U.S.C. § 401(a) (1982) requires all publicly distributed copies of a work protected under the Copyright Act to display a notice of copyright. Omitting the notice will invalidate the copyright unless one of three exceptions applies. An exception to this rule provides that `the copyright is preserved if "the notice has been omitted from no more than a relatively small number of copies . . . distributed to the public." Id. § 405(a)(1).

In the instant case, the evidence introduced at trial showed that, of a total of approximately 25,000 copies, approximately 5,000 contained a Cooling Systems Singapore warranty and a copyright notice, and about 20,000 contained a California Cooling Systems warranty without any copyright notice. The district court assumed that all copies of the catalog in each of the two types resembled the exemplars — one copy of each of the two types of the catalog — produced at trial and thus concluded that the copyright notice had been omitted from more than a relatively small number of copies of the 1979 catalog. E.R. at 29.

This finding is not clearly erroneous. Cooling Systems did not introduce even one copy of a California Cooling Systems catalog bearing a copyright notice. This lapse on Cooling Systems' part can itself be taken as evidence that no such catalog existed. See United States v. Roelof Construction Co., 418 F.2d 1328, 1332 (9th Cir. 1969). In addition, Cooling Systems introduced no evidence indicating that Stuart had introduced an aberrant copy of the California Cooling Systems catalog. Stuart, aided by the absence of a rebuttal by Cooling Systems, provided sufficient proof that Cooling Systems could not use the "small numbers" exception to the notice requirement.

We also reject the argument that registration of the derivative work creates a presumption of validity of the copyright of the underlying work. Our starting point is 17 U.S.C. § 103(b) (1982):

The copyright in a compilation or derivative work extends only to the material contributed by the author of such work, as distinguished from the preexisting material employed in the work, and does not imply any exclusive right in the preexisting material. The copyright in such work is independent of, and does not affect or enlarge the scope, duration, ownership, or subsistence of, any copyright protection in the preexisting material.

(emphasis added); see also H.R.Rep. No. 1476, 94th Cong., 2d Sess. 57, reprinted in 1976 U.S.Code Cong. Ad.News 5659, 5670 ("[C]opyright in a `new version' covers only the material added by the later author, and has no effect one way or the other on the copyright or public domain status of the preexisting material.") (emphasis added). To avoid the force of this provision, Cooling Systems relied on section 410(c), which provides that a registration certificate establishes prima facie validity of the copyright. Using that section as a bootstrap Cooling Systems seeks to create a presumption that all preexisting works bore copyright notices if the derivative work bore one. This argument is meritless. The district court's finding that Cooling Systems never cured its omission of notice in the 1979 catalog, given that Cooling Systems did not introduce proof of cure independent from the section 410(c) argument, is neither clearly erroneous nor infected with legal error. The import of this conclusion is obvious: because Cooling Systems did not alter the arrangement of the facts as first developed in the 1979 catalog, and because the 1979 catalog bore no copyright notice, the arrangement of the 1979 catalog has been dedicated to the public domain. Cooling Systems cannot prevail in its suit for infringement of the arrangement of its 1981 catalog. Cooling Systems also cannot prevail on its argument that the district court should have admitted the later Stuart catalog into evidence. The arrangement of the Cooling Systems catalog, being in the public domain, had no copyright protection and the second Stuart catalog could not have infringed the Cooling Systems catalog. We decline to decide whether the district court erred in refusing to admit the second Stuart catalog into evidence; even if it were error to have refused to admit the catalog, the error would obviously have been harmless.

E. Cooling Systems' Substantial Similarity Claims Were Frivolous.

Because we have determined that the district court did not err in finding that the arrangement of the 1981 Cooling Systems catalog was in the public domain, ordinarily it would not be necessary to reach the substantial similarity issue. But that issue affects the question of attorneys' fees. This necessitates its discussion.

To establish a case for infringement, a plaintiff must show that he owns the copyright, that the defendant had access to the copyrighted work, and that, as between the plaintiff's and the defendant's works, substantial similarity of both the ideas and the expression of those ideas exists. Berkic v. Crichton, 761 F.2d 1289, 1291-92 (9th Cir. 1985), cert. denied, ___ U.S. ___, 106 S.Ct. 85, 88 L.Ed.2d 69 (1985); see also Landsberg v. Scrabble Crossword Game Players, Inc., 736 F.2d 485, 488 (9th Cir.), cert. denied, ___ U.S. ___, 105 S.Ct. 513, 83 L.Ed.2d 403 (1984); Sid Marty Krofft Television Productions, Inc. v. McDonald's Corp., 562 F.2d 1157, 1162 (9th Cir. 1977). Assuming for the moment that Cooling Systems had a valid copyright in the arrangement of its 1981 catalog, and given that Stuart did not dispute either its access to that catalog or its use of the catalog in preparing its own catalog, the remaining issue is whether the district court properly concluded that the catalogs were not substantially similar. We find that the conclusion was not clearly erroneous. Taking into account the limited amount of protectible material in the catalog and the even more limited range of expression available to Stuart, a contrary finding would have been extremely difficult to support.

Copyright law never protects the facts and ideas contained in published works. See Harper Row, Publishers, Inc., v. Nation Enterprises, ___ U.S. ___, 105 S.Ct. 2218, 2224, 85 L.Ed.2d 588 (1985); Mazer v. Stein, 347 U.S. 201, 217, 74 S.Ct. 460, 470, 98 L.Ed. 630, reh'g denied, 347 U.S. 949, 74 S.Ct. 637, 98 L.Ed. 1096 (1954). An author can claim to "own" only an original manner of expressing ideas or an original arrangement of facts. The works at issue here contain a great many unprotectible facts and very little protectible expression of arrangement of those facts. This is not altogether surprising. Catalogs, by definition, are saturated with facts, numbers, and literal depictions of concrete objects. As we emphasized in an only slightly different context, copyright law considers factual works to be fundamentally different from more artistic works: "similarity of expression may have to amount to verbatim reproduction or very close paraphrasing before a factual work will be deemed infringed." Landsberg, 736 F.2d at 488.

Cooling Systems relies heavily on Landsberg's refusal to decide the issue of "whether a work that rephrased in the same order as the original a substantial part of the ideas in another work might be held to infringe that work as a compilation . . . even though none of the rephrasings of the individual ideas would constitute infringement when viewed in isolation." Landsberg, 736 F.2d at 489. It claims that the alleged infringement falls precisely within the grey area that Landsberg refused to decide. Brief for Appellant at 24-25. This contention must fail. Landsberg's principle — that the fewer the methods of expressing an idea, the more the allegedly infringing work must resemble the copyrighted work in order to establish substantial similarity — must govern. Here the range of possible expressions is extremely narrow; it embraces only variations on a catalog arrangement. See also Krofft, 562 F.2d at 1168 ("the scope of copyright expression increases with the extent expression differs from the idea"); cf. Herbert Rosenthal Jewelry Corp. v. Kalpakian, 446 F.2d 738, 742 (9th Cir. 1971) (discussing the "unity of idea and expression" end of the idea-expression continuum). Like the ideas about Scrabble strategy at issue in Landsberg, the facts about replacement radiators cannot be expressed in a wide variety of ways. The district court did not err in noting that the principles of Landsberg were controlling.

It is true, of course, that to whatever extent the expression and arrangement of facts is original, an author is protected against its copying. See, e.g., United States v. Hamilton, 583 F.2d 448, 452 (9th Cir. 1978) (arrangement of information in a map may be original and thus protectible); 1 Nimmer, § 2.11[D], at 2-164. But the author of a factual work ultimately must show that what has been taken from his expression is something more than what "must unavoidably be produced by anyone who wishes to use and restate" the facts that form the greater part of the work. See Landsberg, 736 F.2d at 489.

This Cooling Systems cannot do. For example, Cooling Systems makes much of the fact that both catalogs are arranged in three basic parts: an illustrations section, an OEM (original equipment manufacturer) section, and an applications section. But at trial, its own witness testified that a radiator "`catalog is basically divided into three sections . . . You can compare it to a 3-legged stool. If one is not there you don't have a stool.'" Brief for Appellee at 11 n. 7. Cooling Systems should not now be amazed to find that all three-legged stools do, in fact, have three legs. Even more telling than the witness' testimony is the information expressed in footnote 29 of Appellant's brief:

Prior to the 1979 version of its catalog, [Cooling Systems] had published a 1978 and a 1978/79 catalog. These catalogs were [Cooling Systems'] initial attempts at producing a usable catalog, and proved to be unsuccessful. This was because they were arranged in a manner substantially different from the 1979, 1980 and 1981 catalogs.

Brief for Appellant at 28 (emphasis added). Surely Cooling Systems cannot contend that Stuart, to escape a charge of copyright infringement, must restrict itself to producing a catalog not usable by those for whom it is intended.

The tripartite arrangement of the catalog is thus unprotected material, and the similarity of the gross characteristics of the arrangement is non-infringing. The other similarities that Cooling Systems finds between the catalogs are also either inevitable (and thus non-infringing) or trivial. Cooling Systems, for example, observes that, in several places, both catalogs list automobile makes in alphabetical order. Obviously an alphabetical list is not a protectible form of arranging proper names. Cooling Systems' strongest argument — that common errors, such as inaccurate illustrations of radiators and listings of automobile models that were never manufactured, in the two catalogs are persuasive indicia of copying — is, like its other "substantial similarity" claims, only partially correct. It is true that "courts have regarded the existence of common errors in two similar works as the strongest evidence of piracy," 3 Nimmer, § 13.03[C], at 13-44, but proof of common errors does not obviate the need for proving substantial similarity. Id. Professor Nimmer's treatise disposes of the argument that copying erroneous descriptions of radiator parts or models of cars can constitute infringement: "if only `facts' are copied, this is non-infringing . . . even if such `facts' prove to be erroneous." 3 Nimmer, § 13.03[C], at 13-45 n. 81.

Cooling Systems also errs in its use of the "intrinsic" test for substantial similarity of expression set forth in Krofft, 562 F.2d at 1164. It argues that the ordinary reasonable observer would find that the catalogs are virtually indistinguishable. This misses the point. What is important is not whether there is substantial similarity in the total concept and feel of the works, cf. Berkic, 761 F.2d at 1294, but whether the very small amount of protectible expression in Cooling Systems' catalog is substantially similar to the equivalent portions of Stuart's catalog. Under this standard, the district court's dismissal of this case on the ground that no substantial similarity existed was not clearly erroneous.

F. The Award of Attorneys' Fees to Stuart Was Not an Abuse of Discretion.

Although, in some other circuits, an award of attorneys' fees to the prevailing party in a copyright case does not require a finding of bad faith or frivolity, see, e.g., Original Appalachian Artworks, Inc. v. Toy Loft, Inc., 684 F.2d 821, 832 (11th Cir. 1982); Diamond v. Am-Law Publishing Corp., 745 F.2d 142 (2d Cir. 1984), we predicate an award under 17 U.S.C. § 505 (1982) on such a finding. See Jartech, Inc. v. Clancy, 666 F.2d 403, 407 (9th Cir.), cert. denied, 459 U.S. 879, 103 S.Ct. 175, 74 L.Ed.2d 143, reh'g denied, 459 U.S. 1059, 103 S.Ct. 477, 74 L.Ed.2d 624, second reh'g denied, 463 U.S. 1237, 104 S.Ct. 33, 77 L.Ed.2d 1453 (1983); cf. See v. Durang, 711 F.2d 141, 144 (9th Cir. 1983) (per curiam) (weak argument on substantial similarity not so frivolous as to justify an award of attorneys' fees). The district court did not make an explicit finding of either bad faith or frivolity. The record demonstrates, however, sufficient indicia of bad faith and frivolity to justify the district court's holding. For example, Cooling Systems, to bolster its substantial similarity claim, suggests that Stuart could have arranged its catalog in a wide variety of very impractical ways. These included such fanciful proposals as "list[ing] the automobiles in its applications section alphabetically by models, instead of makes; . . . and, with respect to its OEM cross-references section, list[ing] OEM numbers by automobile model instead of by make." Reply Brief for Appellant at 8 n. 4. To have adopted such arrangements would have made the catalogues virtually useless. Cooling Systems' admission, in its own brief, that its former — and different — arrangement of the catalogs had been a commercial failure amply demonstrates this. See Brief for Appellant at 28 n. 29. Also Cooling Systems waited until virtually the last minute to amend its typographical error in the registration certificate and changed, also at the last minute, the authorship of the catalog to include a foreign author (apparently to avoid Stuart's use of the Manufacturing Clause defense). The district court did not abuse its discretion in awarding attorneys' fees.

G. Attorney's Fees on Appeal Are Justified.

Because of this conclusion, Stuart is entitled to attorneys' fees on appeal as well.

AFFIRMED.