POSNER, Circuit Judge.

Interscholastic high school sports in Illinois, including basketball, are conducted under the aegis of the Illinois High School Association, a private association of virtually all of the state's public and private (including parochial) high schools. A rule of the Association forbids basketball players to wear hats or other headwear, with the sole exception of a headband no wider than two inches, while playing. The principal concern behind this prohibition is that the headwear might fall off in the heat of play and one of the players might trip or slip on it, fall, and injure himself.

This rule is challenged in the present case as an infringement of the religious freedom of orthodox Jews. According to a stipulation between the parties, orthodox Jewish males are required by their religion "to cover their heads at all times except when they are (a) unconscious, (b) immersed in water or (c) in imminent danger of loss of life." There is no exception for playing basketball. Orthodox Jews who play basketball comply, or at least try to comply, with this requirement by wearing yarmulkes (small skull caps that cover the crown of the head) fastened to the hair with bobby pins. Ordinarily a yarmulke just perches on the head; the bobby pins are an acknowledgment of the yarmulke's instability on a bobbing head. But bobby pins are not a secure method of fastening; yarmulkes fastened by them fall off in the heat of play with some frequency. The Association has interpreted its rule to forbid the wearing of yarmulkes during play; and the plaintiffs in this lawsuit — two orthodox Jewish high schools in Chicago, the members of their interscholastic basketball teams, and the members' parents — contend that this interpretation forces them to choose between their religious observance and participating in interscholastic basketball, which as it happens is the only interscholastic sport in which the two schools participate.

The district court held that the Association is an arm of the state for purposes of the Fourteenth Amendment, that the hazards posed by yarmulkes are too slight to justify putting the plaintiffs to the choice we have just mentioned, and therefore that the rule, as applied to prohibit the wearing of yarmulkes while playing basketball, violates the free-exercise clause of the First Amendment, which was held in Cantwell v. Connecticut, 310 U.S. 296, 303-04, 60 S.Ct. 900, 903-904, 84 L.Ed. 1213 (1940), to be applicable to the states by virtue of the due process clause of the Fourteenth Amendment. 527 F. Supp. 637 (N.D.Ill. 1981).

The Association no longer contests the finding that it is an arm of the State of Illinois for purposes of the Fourteenth Amendment. Although the Association is nominally a private organization, public high schools comprise the bulk of its membership and dominate its decisionmaking. Since there is no issue of state action before us, we need not consider the district court's application of the principle of collateral estoppel to bar the Association from denying that it is an arm of the state for purposes of the Fourteenth Amendment. Our silence is not to be construed as approval or disapproval of the district court's analysis of this question.

The First Amendment, so far as is relevant to this case, provides that "Congress shall make no law . . . prohibiting the free exercise [of religion]." Read literally (after substituting "Illinois High School Association" for "Congress" and "rule" for "law"), this language would not forbid a regulation secular in purpose (the purpose of the no-headwear rule is to promote safety); general in application; not motivated by antipathy to any religious group on which the regulation might bear heavily or by sympathy for a competing group (there is no suggestion of any such motivation here); and that does not actually prohibit a religious observance but merely makes it more costly by forcing the observant to give up some government benefit (here, participation in an interscholastic sport sponsored by an arm of the state). Wisconsin v. Yoder, 406 U.S. 205, 92 S.Ct. 1526, 32 L.Ed.2d 15 (1972), on which the plaintiffs rely heavily, involved a state law that forced Amish children to attend school, contrary to their religion. The counterpart in this case would be a state law that forbade people to cover their heads, wherever they were or whatever they were doing, with no exception for orthodox Jews. Cf. Moskowitz v. Wilkinson, 432 F. Supp. 947 (D.Conn. 1977). The no-headwear rule does not do this; it forces orthodox Jews to choose only between keeping their heads covered and playing interscholastic basketball.

But whatever the literal or for that matter the original meaning of the free-exercise clause, the Supreme Court has interpreted it to require the government, when it can do so without too much cost or inconvenience, to bend its regulations — even when they are secular, general, nondiscriminatory, and do not forbid but merely burden a religious observance — to spare religious people the painful choice between giving up a part of their religious observance and giving up a valuable government benefit. In Sherbert v. Verner, 374 U.S. 398, 83 S.Ct. 1790, 10 L.Ed.2d 965 (1963), a Seventh-Day Adventist was fired by her employer because she would not work on Saturdays — her religion forbade her to do so. She applied for unemployment compensation. It was denied on the ground that her refusal to work on Saturdays constituted a failure, without good cause, to accept available suitable work when offered, a condition under state law for receiving unemployment compensation. The Supreme Court held that this denial placed a burden on the plaintiff's exercise of her religion that was disproportionate to the state's interest, described as the avoidance of "fraudulent claims by unscrupulous claimants feigning religious objections to Saturday work. . . ." 374 U.S. at 407, 83 S.Ct. at 1795.

Sherbert and the cases following it require a comparison of two burdens: the burden on the person who is seeking a government benefit of being denied the benefit as the price of observing his religion, and the burden on the government of extending the benefit to someone who fails to meet the usual requirements for eligibility. See, e.g., Giannella, Religious Liberty, Nonestablishment, and Doctrinal Development, 80 Harv.L.Rev. 1381 (1967); Note, Religious Exemptions under the Free Exercise Clause: A Model of Competing Authorities, 90 Yale L.J. 350, 351-62 (1980). The more valuable the benefit to the claimant and hence the greater the burden on him of forgoing it in order to continue to observe his religion, the greater must be the burden on the government of relaxing the conditions it places on that benefit for a refusal to make an exception for the claimant to survive a challenge based on the First Amendment. Free exercise of religion does not mean costless exercise of religion, but the state may not make the exercise of religion unreasonably costly.

The benefit that the plaintiffs seek in this case is participation in interscholastic basketball games; for so far as appears the rules of the Illinois High School Association do not forbid the wearing of headwear in any other sport, and anyway the plaintiffs do not want to participate in any of the other interscholastic sports regulated by the Association. Windsor Park Baptist Church, Inc. v. Arkansas Activities Ass'n, 658 F.2d 618 (8th Cir. 1981), held that it was not a violation of the free-exercise clause to exclude a Baptist school from participating in all the interscholastic sports sponsored by the Arkansas counterpart to the Illinois High School Association because the school refused on religious grounds to seek accreditation by state educational authorities as required by state law. But the fact that the burden on religious observance was greater in Windsor than in the present case is not decisive. We must also compare the burden on the states of accommodating their interests to those of the religious claimants. As under any balancing test, each case tends to be sui generis, so that the principal value of precedent is to identify the interests that must be weighed and to tell us whether, in weighing them, we should place our thumb on one pan or the other. Sherbert indicates that our thumb should be on the claimant's pan, because it says that the state's interest must be "compelling" to outweigh the claimant's. 374 U.S. at 403, 406, 83 S.Ct. at 1793, 1795. See also Thomas v. Review Bd. of Indiana employment Security Div., 450 U.S. 707, 718, 101 S.Ct. 1425, 1434, 67 L.Ed.2d 624 (1981). Yoder, however, suggests that a secular regulation is permissible unless it "unduly burdens" the free exercise of religion. See 406 U.S. at 220, 92 S.Ct. at 1535.

But in the view we take of this case we do not have to choose between these formulations, assuming they really are different. A court, before attempting to balance competing interests, must define them as precisely as it can, since in the process of definition it may become apparent that there is no real conflict. The concept of "false conflict," a major theme in the modern scholarship on conflict of laws, see, e.g., Cavers, The Choice-of-Law Process 89-92 (1965), has, we think, an application to constitutional adjudication in general and to this case in particular. The conflicting claims of church and state are a source of some of the bitterest and most divisive controversies in our society. Weigh them and choose we shall if we must, but we want first to satisfy ourselves that the claims really are irreconcilable.

The parties have argued this case to us as if the religious obligation that was in conflict with state regulation was an obligation while playing basketball to wear a yarmulke fastened to your hair by bobby pins. But that is not what the stipulation says, and while we are not Talmudic scholars we are reasonably confident, and the plaintiffs' counsel acknowledged at oral argument, that the precise nature of the head covering and the method by which it is kept on the head are not specified by Jewish law. The wearing of a yarmulke — which by its size and position is liable to fall off in any activity involving sudden movement — is conventional rather than prescribed; some orthodox Jews prefer to wear an ordinary hat instead. The affixing of the yarmulke to the head (more precisely, the hair) by bobby pins is even more obviously a convention rather than a religious obligation, and it happens to be an inherently insecure method of keeping the yarmulke attached during basketball play.

If the Talmud required basketball players to wear yarmulkes attached by bobby pins, there would be a conflict with the state's interest in safety. But it does not, so it would seem that all the plaintiffs have to do to obviate the state's concern with safety is to devise a method of affixing a head covering which will prevent it from falling off during basketball play. We are not the people to devise the method — to say that yarmulkes should be equipped with chin straps or sewn to headbands or replaced by some form of head covering that fits the head more securely. But we are reasonably sure that a secure head covering exists or can be devised at trivial cost without violating any tenet of orthodox Judaism; that, on the facts of this case at least, bobby pins do not implicate First Amendment values.

Of course the Illinois High School Association might decide that its rule forbade even a completely secure head covering (as, indeed, the language of the rule suggests) and might also, if it so concluded, refuse to change the rule. A letter from an official of the Association, and testimony of Dr. Edward Steitz (who we are told is "Mr. Basketball"), provide some support for this supposition, though the point was not pressed below. But if the Association proves to be so obdurate — if it refuses to accommodate the indisputably sincere beliefs of a religious group though it can do so at no cost to the only objective, safety, that the rule in question is claimed to have — it will be standing on constitutional quicksand. Even if the interest in participating in interscholastic basketball is a slight one, a question we need not decide, it would by definition outweigh the burden on the state of accommodating that interest if there were no burden at all.

But by the same token the plaintiffs would be on weak ground if they claimed a constitutional right to wear yarmulkes fastened insecurely with bobby pins, on the theory that the state has no interest in more secure head coverings. It is true, as the district court found, that the Association's efforts to prove that insecurely fastened yarmulkes pose a substantial safety hazard were unconvincing. All it could prove was the yarmulkes fall off basketball players' heads once or twice a game, on average, despite the bobby pins, and that in principle any loose object on the floor can cause a player to slip or trip and thereby fall and injure himself. The Association was unable to produce an authenticated instance of a fall caused by yarmulke. But we do not consider this failure of proof quite so devastating as the district court did. The state need not await disaster to regulate safety; the effort of the Association to take preventive measures against injury before a history of accidents has been complied is rather to be commended than condemned. Because the rule, which was drafted by the national federation of state high school associations, is in force in most of the nation and not just in Illinois, experience with interscholastic basketball games in which players wear yarmulkes has been limited. And falls are such a common part of basketball that when someone does fall no one stops the game to investigate the cause. As a result we do not know how many of the falls that occur in games where players are wearing yarmulkes are due to that fact — we do not even know whether falls are more common in such games than in games where the Association's rule is enforced.

The district court thought the fact that the Association once had an exception to its no-headwear rule for "soft barrettes," and repealed it during the course of this litigation, proves that the Association's concern with the safety hazard posed by yarmulkes is spurious. But the exception was not irrational, so even if it was repealed for purely tactical reasons this would not show that the Association has no reason to be concerned about loose yarmulkes. Barrettes, which are worn by girls to keep their hair in place, may fall on the floor, just like yarmulkes, but until they do so they keep the wearer's hair out of her eyes and make it less likely that she will collide with someone or fail to see an obstacle on the floor. Eyeglasses, which also are permitted by the Association's rules though they sometimes fall off, reduce the likelihood of a collision or a fall. A headband, the only form of headwear permitted, prevents sweat from getting in the eyes or falling on the floor and making it slippery. Yarmulkes do not have the safety-enhancing properties of barrettes, headbands, and eyeglasses. That is why, incidentally, the no-headwear rule does not violate the equal protection clause of the Fourteenth Amendment just because glasses and headbands are permitted — the plaintiffs' alternative ground, not addressed by the district court, for upholding that court's judgment.

While we are unwilling to dismiss as spurious the safety concern behind the application of the Association's rule to yarmulkes fastened only by bobby pins, we do not think it is great enough to justify the state's placing a heavy burden on religious observance. But virtually by definition it has sufficient substance to outweigh a nonexistent burden on religious observance. And the burden would be nonexistent if the only thing the rule forbade was the wearing of an insecurely mounted yarmulke since, as we said earlier, there appears to be nothing in Jewish law that requires that the head covering take that form. If the plaintiffs can totally allay the state's safety concern at zero, or practically zero, cost to them, they must do so. Otherwise the state's concern, even if relatively slight, will be a compelling interest in relation to the (non)burden on the plaintiffs' religious freedom.

As the plaintiffs had the burden of proving that their First Amendment rights were infringed by the Association's no-headwear rule, we are constrained on this record to conclude that they failed to make out a case and that the judgment in their favor must be vacated. As we have explained, they have no constitutional right to wear yarmulkes insecurely fastened by bobby pins and therefore they cannot complain if the Association refuses to let them do so because of safety concerns which, while not great, are not wholly trivial either. But it does not follow that the complaint should be dismissed. The district court should retain jurisdiction so that the plaintiffs can have an opportunity to propose to the Association a form of secure head covering that complies with Jewish law yet meets the Association's safety concerns. If the Association refuses to interpret or amend its rule to allow such a head covering to be worn by orthodox Jews, the district court should then proceed to determine, consistently with the analysis in this opinion, the plaintiffs' right to have the rule enjoined as a violation of their religious freedom.

We put the burden of proposing an alternative, more secure method of covering the head on the plaintiffs rather than on the defendants because the plaintiffs know so much more about Jewish law. The stipulation is singularly unilluminating about the content of that law, and because of the importance of avoiding false conflicts in constitutional adjudication we deprecate it as a basis for the decision of this case. Read literally, the stipulation would prevent orthodox Jews from getting haircuts, would require them to wear a hat or yarmulke to bed (though it could be removed after they fell asleep), and might even forbid them to play basketball while wearing yarmulkes fastened only by bobby pins, given the high probability that the yarmulke will fall off at some point during the game (or during the season) and cause — it would seem — a violation of religious law. To the extent that such questions of religious interpretation prove actually relevant to this case they should be addressed, in the first instance at least, by the plaintiffs when they propose to the Association in the further proceedings that we envisage on remand a more secure method of head covering. And if, despite counsel's representation at oral argument, we are incorrect in believing that Jewish religious law permits a more secure head covering than a yarmulke fastened only by bobby pins, this also can be raised on remand.

For the additional guidance of the district court we shall consider very briefly its suggestion that the Association has a heavier burden of justifying any restriction that it may place on the free exercise of religion than a formal agency of the State of Illinois would have. The court acknowledged that it had no precedent for this suggestion, and we think it unsound. The Fourteenth Amendment is addressed to state action, and we cannot understand how it could be that the more attenuated was the state's involvement in an alleged violation of constitutional rights the stricter would be its constitutional obligations. It is true that if the governing board of the Illinois High School Association were elected by the people of Illinois rather than by the (mainly) public schools that comprise the membership of the Association, it would be a more representative, a more popular, institution. But we differ with the district court in thinking that this would entitle it to a lower standard of constitutional scrutiny. The free-exercise clause, like so much else in the Constitution, is designed to protect minorities, and their rights are as much endangered by popular assemblies as by quasi-private voluntary associations — maybe more so. The theory of the Bill of Rights is not Populism; and constitutional law is sufficiently complicated already without separate standards based on the representativeness of the agency alleged to be violating constitutional rights.

VACATED AND REMANDED.

On Petition for Rehearing

The appellees have filed a petition for rehearing with suggestion for rehearing en banc. Since the judges of the original panel have voted to deny the petition (with Judge Cudahy dissenting), and since none of the judges of the court in regular active service has requested a vote on the petition, it is denied. But we think it may clarify our original opinion to comment briefly on three of the grounds on which rehearing was sought.

We are accused of having failed to apply the clearly-erroneous rule to the district court's finding that insecurely fastened yarmulkes do not pose a substantial hazard to basketball players. That rule, however, is designed for the review of findings of "historical," not "legislative," fact. Legislative facts are those general considerations that move a lawmaking or rulemaking body to adopt a rule, as distinct from the facts which determine whether the rule was correctly applied. There is no question that insecurely fastened yarmulkes are within the scope of the Illinois High School Association's no-headwear rule; the question is whether the Association's concern with safety is substantial enough to support the rule as so interpreted; and a fact that goes to the reasonableness of a rule or other enactment is a classic example of a legislative fact, to which as we have said the clearly-erroneous standard does not apply.

The petition for rehearing complains that in our opinion we "scrutinize[d] the sincere religious beliefs of the plaintiffs." We did not. We expressed doubt whether the stipulation entered into by the parties provided an intelligible account of those beliefs, but on the crucial issue of belief — whether Jewish law requires Jewish males to play basketball wearing only insecurely mounted yarmulkes — we relied on the statement of the plaintiffs' counsel at oral argument that Jewish law does not specify the method of head covering and would not be violated by a secure method.

Finally and most important, the petition argues that we placed the burden of "accommodating" competing sacred and secular interests on the religious claimants. We did not. We understand "accommodation" in this context to refer to a giving up in whole or in part of some religious practice, or conversely the giving up in whole or in part of some secular obligation, in order to give effect to the competing interest. If we had held that the Association's concern with safety requires that the plaintiffs abandon either interscholastic basketball or adherence to the tenets of their faith, that would be requiring the plaintiffs to "accommodate" their religious claims to the interests asserted by the state. But we did no such thing. We placed on the plaintiffs only the burden of demonstrating that there is in fact a conflict between the state's interest in safety and their interest in complying with all the requirements of Jewish law. If they can comply fully with all those requirements yet still meet fully the state's concern with safety, as by wearing a yarmulke securely fastened to the head, then they would not be accommodating their religious beliefs to secular commands because as we have emphasized there appears to be no obligation in Jewish law to cover the head with a cap likely to fall off during basketball play. Only if it should turn out that the plaintiffs cannot devise a secure head covering that will satisfy simultaneously the requirements of Jewish law and the state's legitimate concern with safety in basketball play would the question of who has the burden of accommodation arise.