EASTERBROOK, Chief Judge.

New Albany DVD operates an adult store in New Albany, Indiana. It does not provide live or recorded entertainment on site. Customers buy books, magazines, or videos, which they read or watch at home. Plaintiff bought land for this operation in 2003, secured all necessary licenses, and renovated the site's store to meet its requirements. The land was properly zoned for the business it proposed to operate. A final inspection was scheduled for February 19, 2004. But the City refused to carry out that inspection, so plaintiff could not obtain the certificate of occupancy needed to open its doors.

That very day the City Council enacted a six-month moratorium on new adult businesses. In March 2004 the Council amended the zoning rules to forbid any "sexually oriented business" at plaintiff's site. (This phrase includes a book or video retailer if more than 30% of its inventory meets the City's definition of "sexually oriented"; plaintiff's inventory qualifies.) The law prohibits a sexually oriented business from operating within 1,000 feet of a church or any tract zoned for residential use. Plaintiff's store is 175 feet from the nearest church and 115 feet from the site of a proposed residential building.

In this suit under 42 U.S.C. § 1983, plaintiff contends that New Albany's ordinance violates the first amendment (applied to the states by the fourteenth) because it is based on the books' and videos' content or subject matter; because it is inadequately justified by proof of adverse secondary effects and therefore cannot find shelter under the holdings of Los Angeles v. Alameda Books, Inc., 535 U.S. 425, 122 S.Ct. 1728, 152 L.Ed.2d 670 (2002), and Renton v. Playtime Theatres, Inc., 475 U.S. 41, 106 S.Ct. 925, 89 L.Ed.2d 29 (1986); and because it is not narrowly tailored to the City's justification. Plaintiff also argues that, as a matter of Indiana law, it is entitled to operate for two years as a nonconforming use, because the renovations were completed before the zoning ordinance was amended and the store would have opened before the zoning change had the City conducted the final inspection on schedule. The district court held that the ordinance likely is unconstitutional because not narrowly tailored to its purpose. 362 F.Supp.2d 1015 (S.D.Ind. 2005). The court also concluded that Indiana law entitles plaintiff to the two-year grace period. An injunction issued in January 2005 allowing plaintiff to open its store.

The parties have devoted considerable attention to the state-law question on appeal, but it has no continuing import because the two years have expired. Plaintiff has been able to operate its store under the protection of the district court's holding that the zoning rules likely violate the Constitution; it makes no difference whether state law also would have allowed the store to operate for two years.

The injunction should not have issued, however — at least, it should not have issued on the ground that the district court gave. Although Alameda Books and Playtime Theatres hold that regulation of adult businesses must be tailored to the justification for the regulation, these decisions also sustain laws that are no better tailored, and may well be more restrictive, than New Albany's. See also, e.g., Richland Bookmart, Inc. v. Knox County, 555 F.3d 512 (6th Cir. 2009); Fantasyland Video, Inc. v. San Diego, 505 F.3d 996 (9th Cir. 2007); Matney v. Kenosha, 86 F.3d 692 (7th Cir. 1996). See also Ben's Bar, Inc. v. Somerset, 316 F.3d 702 (7th Cir. 2003). Plaintiff does not contend that a 1,000-foot dispersal requirement leaves too little space for it (and other adult establishments) to operate in portions of the City suited to bookstores. See Illinois One News, Inc. v. Marshall, 477 F.3d 461 (7th Cir. 2007). New Albany maintains, and plaintiff does not deny, that more land is available for adult establishments than is put off limits by this ordinance.

The district court faulted New Albany for banning adult establishments within 1,000 feet of land zoned for housing and suggested that a more appropriately tailored ordinance would limit the rule to occupied residences. But there is no doubt that plaintiff's premises are within 200 feet of a church, so it is unaffected by the distance-to-residential-land rule. It is unaffected, for that matter, by the difference between a 1,000-foot dispersal rule and a 250-foot dispersal rule. The district judge next suggested that New Albany allow the bookstore to be near a church but require it to close while services are being held. Such a privileged position for religious worship would cause problems of its own, see Larkin v. Grendel's Den, Inc., 459 U.S. 116, 103 S.Ct. 505, 74 L.Ed.2d 297 (1982), unless there were similar closing requirements when schools and other secular establishments were open.

No appellate court has required a city to adopt a rule of the kind that the district court thought necessary. "Narrow tailoring" does not mean that the ordinance must be the least restrictive possible regulation. See Ward v. Rock Against Racism, 491 U.S. 781, 109 S.Ct. 2746, 105 L.Ed.2d 661 (1989). When some regulation is justified, a city has considerable discretion on matters of detail. The sort of zoning rule that New Albany enacted has been too widely used, and too often sustained, to be upset as "not narrowly tailored."

This does not mean, however, that the injunction must be reversed, for a prevailing litigant is entitled to defend its judgment on any ground preserved in the district court, even if the district judge rejected that argument. Plaintiff defends its judgment with the argument that New Albany has not established that book and video stores offering only take-home items cause any untoward secondary effects. The Supreme Court in Alameda Books and Playtime Theatres held that proof of such effects is essential if municipalities regulate adult establishments differently from the way they regulate other similar businesses — for the sellers of books and movies enjoy constitutional protections that sellers of snow shovels, shoes, and parakeets do not.

In the district court, New Albany relied on studies conducted in cities across the country. Many of these show that a concentration of adult businesses in a part of a city is associated with higher crime and lower property values nearby. As we observed in Annex Books, Inc. v. Indianapolis, 581 F.3d 460, 2009 WL 2855813 (7th Cir. 2009), however, these studies principally reflect the effects of adult businesses that offer live entertainment or peep shows; they do not necessarily demonstrate that businesses selling books and DVDs have the same consequences for morals offenses (prostitution, lewd exhibition) or other kinds of crime. New Albany's own expert "conceded that he knows of no research that shows . . . effects for various subclasses of businesses," such as plaintiff's retail-only store. 362 F.Supp.2d at 1021.

Recognizing that prior studies had lumped bookstores, peep shows, and exotic dancing establishments together, New Albany offered some anecdotal justifications in the district court. It cited testimony in some earlier cases by people complaining about pornographic litter near adult bookstores, and it suggested that these stores may expose their customers to thefts. The former line of argument rests on the fact that some customers are bound to throw away wrappers, which may have images inappropriate for children. The "theft" line of argument starts with the premise that many customers of adult establishments pay in cash, which makes them a target for thieves.

The theft argument is paternalistic. Why can't customers make their own assessments of risk? The norm under the first amendment is that government must combat harm to readers with disclosures rather than prohibitions of speech. See, e.g., Virginia State Board of Pharmacy v. Virginia Citizens Consumer Council, Inc., 425 U.S. 748, 96 S.Ct. 1817, 48 L.Ed.2d 346 (1976); American Booksellers Ass'n v. Hudnut, 771 F.2d 323 (7th Cir. 1985), aff'd mem., 475 U.S. 1001, 106 S.Ct. 1172, 89 L.Ed.2d 291 (1986). Just as there is no hecklers' veto over speech, there is no "thieves' veto." The police must protect the readers from the hecklers or thieves, rather than ease their workload by forbidding the speech.

Anyway, if an adult bookstore located 200 feet from a church attracts thieves, won't a bookstore located 1,500 feet from a church do the same? Maybe the City's concern is for the worshippers, who may become the thieves' targets when video buyers are unavailable. But if that's so, the City needs some evidence that thefts from passers by are a serious problem — and a more severe problem for outlets near churches than for outlets farther away. As the plurality opinion in Alameda Books put it:

[A] municipality [cannot] get away with shoddy data or reasoning. The municipality's evidence must fairly support the municipality's rationale for its ordinance. If plaintiffs fail to cast direct doubt on this rationale, either by demonstrating that the municipality's evidence does not support its rationale or by furnishing evidence that disputes the municipality's factual findings, the municipality meets the standard set forth in [ Playtime Theatres]. If plaintiffs succeed in casting doubt on a municipality's rationale in either manner, the burden shifts back to the municipality to supplement the record with evidence renewing support for a theory that justifies its ordinance.

535 U.S. at 438-39, 122 S.Ct. 1728. New Albany has not supplied evidence that "fairly supports" the idea that adult bookstores located near churches or residences attract thieves who then steal from the local denizens as well as the stores' customers. We don't say that the City will be unable to produce this evidence, but the lack of good evidence to this effect in the record — coupled with evidence implying that take-home adult stores do not have adverse secondary effects — is enough to require an evidentiary hearing. Our opinion in Annex Books expands on this reasoning, which need not be repeated here.

Pornographic litter is the City's other principal basis. The printed word often is tossed away, but litter-control justifications have fared poorly as reasons to regulate pamphlets and other written materials. Compare Schneider v. State, 308 U.S. 147, 60 S.Ct. 146, 84 L.Ed. 155 (1939), with Los Angeles v. Taxpayers for Vincent, 466 U.S. 789, 808-10, 104 S.Ct. 2118, 80 L.Ed.2d 772 (1984). Perhaps smutty litter should be judged by different standards, but first it is necessary to know how serious the problem is. That one pedodontist in Spokane complained about litter from one bookstore, see World Wide Video of Washington, Inc. v. Spokane, 368 F.3d 1186, 1197 (9th Cir. 2004), does not do much to establish that this is a serious problem in New Albany (or even in Spokane). The volume of complaints exceeds the number of genuine problems. There are thousands of adult bookstores; it should be easy to find out how much litter they generate, how much of this litter falls into the hands of minors, and whether this is a materially greater problem when one store carries 40% adult books than when lots of stores carry 10% apiece. (Many a convenience store, newsstand, or video rental outlet has an adult nook, which escapes regulation under New Albany's statute.) Plaintiff has been in operation for a while now; is sexually themed litter a problem near its store?

If litter is a problem, can it be curtailed without an equal curtailment of speech? Justice Kennedy, whose vote was essential to the judgment in Alameda Books, and whose views therefore constitute the holding of that case, stated that the reduction in adverse secondary effects may not be achieved just by curtailing speech. "A city may not assert that it will reduce secondary effects by reducing speech in the same proportion." 535 U.S. at 449, 122 S.Ct. 1728. New Albany's "litter" justification comes perilously close to this, because the amount of pornographic litter may depend linearly on the volume of adult materials sold. The only way to cut litter by 10% may be to reduce sales by 10%, and such a justification would fail under Justice Kennedy's approach.

New Albany may be able to resuscitate its anti-litter rationale by showing that the zoning law moves litter to where children (and sensitive pedodontists) won't see it. Placing businesses where they will be equally productive but less harmful is a lawful objective of zoning. Alameda Books, 535 U.S. at 446-47, 122 S.Ct. 1728 (Kennedy, J., concurring). But, for this justification to work, it will be necessary to establish (a) how much sex-oriented litter an adult bookstore generates; (b) who is likely to see that litter in the parts of New Albany where adult bookstores are allowed to operate; and (c) how much adult litter will remain in New Albany's central business area (generated by adult corners of other businesses) if plaintiff is exiled to an industrial district or highway. Otherwise evidence about litter cannot support the sort of regulation that New Albany has enacted.

The district court needs to take evidence and apply intermediate scrutiny to New Albany's ordinance. The case is remanded for proceedings consistent with this opinion and Annex Books. The injunction should remain in place pending the outcome of this hearing.