EASTERBROOK, Circuit Judge.

Both Western Casualty & Surety Co. and Western World Insurance Co. issued policies to the City of Crystal Lake, Illinois. Western Casualty’s policy covered, among other things, “discrimination excluding intentional acts.” Western World’s covered “wrongful acts,” which it defined to mean “any actual or alleged error ... or act or omission or neglect or breach of duty including misfeasance, malfeasance and nonfeasance by an Insured.” The policy then excluded “loss in connection with any claim ... based upon or arising out of ... (7) the willful violation of statute or ordinance committed by or with the knowledge or consent of the Insured.”

Crystal Lake refused to permit the construction of some subsidized, low-income housing. The owner of the land and the sponsors of the project brought suit, contending that the City’s refusal violated the Equal Protection Clause of the Fourteenth Amendment' and several federal statutes, including 42 U.S.C. §§ 2000d and 3601. The complaint alleged that the City intentionally discriminated against low-income prospective tenants; it also alleged that because black and Hispanic people are *383 more likely to have low incomes, the City’s decision had a disparate effect on these groups that violated both Constitution and statutes.

The City notified both insurers. Western World denied all liability and refused to defend; Western Casualty, while reserving its position on liability, undertook the defense. Ultimately the City settled the suit. It consented to injunctive and declaratory relief, and Western Casualty paid the plaintiffs’ legal expenses of $86,867.87. Western Casualty also paid counsel $23,645.50 for defending the City. In this diversity action Western Casualty seeks compensation from Western World for the costs of litigating and settling the suit against the City.

This case is governed, the parties agree, by the common law of Illinois. Illinois permits a suit by one insurance company against another even though the insured has suffered no loss. E.g., Royal Globe Insurance Co. v. Aetna Insurance Co., 82 Ill.App.3d 1003, 38 Ill.Dec. 449, 403 N.E.2d 680 (1st Dist.1980). Although the Illinois cases involve suits by excess carriers against defaulting primary carriers, their rationale applies as well to suits among primary carriers. The state seeks to encourage all carriers to participate in the initial proceedings, and as the state courts have found, it is a bad idea to inform insurance carriers that whichever is least faithful to its obligation to the insured will escape all liability as long as a responsible carrier covers the loss. See Aetna Casualty & Surety Co. v. Coronet Insurance Co., 44 Ill.App.3d 744, 3 Ill.Dec. 371, 358 N.E.2d 914 (5th Dist.1976).

Western World’s principal defense was based on general condition (i) of its policy, which provides that if the City “has other insurance insuring against a loss covered by this policy, the insurance provided by this policy shall apply in excess of such other insurance.” Condition 6 in Western Casualty’s policy states that “[t]he insurance afforded by this policy is primary insurance____ When ... the insured has other insurance which is stated to be applicable to the loss on an excess or contingent basis, the amount of The Western’s liability under this policy shall not be reduced by the existence of such other insurance.” Western Casualty settled the suit against the City within the limits of its policy. Western World therefore contends that it is not liable; it is an excess insurer, and there is no excess.

The district court rejected this argument because Western Casualty’s policy covers “discrimination excluding intentional acts.” (The parties and the district court treat this as meaning “discrimination except intentional discrimination.” This converts “intentional acts” into a term of legal art, “intentional discrimination.” We have no reason to reject this assumption of all concerned.) To the extent the loss stemmed from intentional discrimination, the court held, Western World could be liable under its coverage of “malfeasance” as a primary carrier. In a second opinion, however, the district court held that the exclusion of “willful violation[s] of statute” from Western World’s coverage applied to the claims in the suit against the City. Western World therefore prevailed, and. Western Casualty appeals.

Western Casualty argues that the district court’s interpretation drains Western World’s coverage of “malfeasance” of any content. Recent cases holding that wilful violations of law are a subset of intentional violations support this position. A person may intend the acts and desire the consequences, making the conduct intentional, see Personnel Administrator of Massachusetts v. Feeney, 442 U.S. 256, 279, 99 S.Ct. 2282, 2296, 60 L.Ed.2d 870 (1979), without knowing that this violates the law or being reckless on this score, a requirement of wilfulness, see Trans World Airlines, Inc. v. Thurston, — U.S.-, 105 S.Ct. 613, 625-26, 83 L.Ed.2d 523 (1985). The construction of “wilful” in Thurston, if applied to Western World’s policy, would permit it to cover at least some discrimination of the sort not covered by Western Casualty’s policy.

*384 We need not decide whether Western World’s policy covered a category of intentional but not wilful discrimination, however, unless the district court’s conclusion that the two policies both create primary insurance is correct. We are convinced that it is not. Western World’s policy is excess if there is other insurance “against a loss covered” by the policy. The district court assumed that the excess clause operates on each theory of liability, rather than each “loss.” According to the district court, Western Casualty’s policy covers unintentional discrimination (“disparate impact”), which made Western World’s policy excess on that theory, but only Western World’s policy covers intentional discrimination, which made it a primary insurer on that theory of liability. A “loss” is not the same as a theory of liability, however.

The difficulty in this case arises from the different designations used by the excess insurance clause and the exclusions in Western World’s policy. The excess insurance clause depends on whether a “loss” is “covered” by some other policy. The exclusions depend on the theories of liability that underlie a claim. When a claim is founded on (or a loss caused by) two or more acts, one included and others excluded, what happens?

If the case goes to trial, and the plaintiff wins on one theory while losing on another, then it is easy to tell which policy governs. But most cases are settled, as this was. The settlement did not apportion damages among theories of liability. The plaintiffs received an injunction, not damages. They suffered a single injury (the denial of the right to build the low-income housing) and obtained a single remedy. They did not care on what ground they won, so long as they won.. The award of attorneys’ fees was justified by the fact that the plaintiffs prevailed, not by any particular theory of the City’s liability. It is simply impossible to know the basis of liability — if the City was liable at all. It may have settled the case, although it had committed no wrong, to end the continued expense and drain of its officials’ time that litigation entails.

We have decided under Illinois law a case closely related to this one, although the parties did not cite the case to the district court or to us. Home Insurance Co. v. Certain Underwriters at Lloyd’s, 729 F.2d 1132 (7th Cir.1984), deals with overlapping policies. One was a comprehensive policy, the other a policy limited to harm caused by the design of a petroleum-refining process. An explosion at the refinery injured an employee, whose suit contended that the refinery was negligently designed, built, and operated. That suit was settled, and inevitably the question arose which policy covered the loss. The underwriters of the design policy said “not us,” because the policy was limited to a single theory and the suit was not. The court pointed out that it was impossible to tell the ground of the settlement and concluded that because there was a single loss (one injury), and both policies applied to the plaintiff’s claims, both insurers would bear liability according to the operation of the excess clauses in the policies. 729 F.2d at 1134. Cf. Chambers Gasket & Manufacturing Co. v. General Insurance Co., 29 Ill.App.3d 998, 331 N.E.2d 203 (1st Dist.1975).

In this case, as in Home Insurance, there was a single loss and multiple theories of liability. Here, as in Home Insurance, the case was settled in a way that makes it impossible to know what theory of liability (if any) was dispositive. Western Casualty covered the “loss.” Having settled the suit and made impossible any determination of the basis of liability, Western Casualty had to indemnify the City. It was fully liable. As a result, here, as in Home Insurance, the insurers must bear liability according to their excess clauses. The clause in Western World’s policy provides that the policy is “excess” when the “loss” is covered by another policy. This loss was, so Western World’s policy is excess.

The conclusion that an excess clause referring to a “loss” comes into play if another policy applies to that same “loss,” albeit on a different theory of liability, is not just an arid application of logic. The exclusions *385 in an insurance policy serve a different function from the excess clause, and it is helpful to separate the two.

The exclusions of liability help control moral hazard. Once a person has insurance, he will take more risks than before because he bears less of the cost of his conduct. A person with insurance on his driving may take less care on the road. Insurance therefore tends to increase the likelihood that the insured risks will come to pass. Sometimes the increase is likely to be small — the driver is probably more interested in his own neck than in small increases in his financial liability. Other risks, however, could be affected more substantially. If an insurance policy were to cover a city’s wilful racial discrimination, the people making policy for the city could indulge their own preference for discrimination at little risk to themselves. The city would pay in higher rates, but given the insurance each employee would be more likely to discriminate. Many insurance policies therefore exclude wilful misconduct, and moral hazard also is the basis of the legal rule that insurance against some kinds of wilful conduct is unlawful. E.g., Rubenstein Lumber Co. v. Aetna Life & Casualty Co., 122 Ill.App.3d 717, 78 Ill.Dec. 541, 462 N.E.2d 660 (1st Dist.1984).

The excess insurance clause, on the other hand, has nothing to do with moral hazard. It is designed to apportion liability among insurance carriers, not to limit the aggregate liability. The primary carrier bears the initial risk. Because most claims are for small amounts (relative to the limits of liability), the primary carrier can defend and pay these claims in the ordinary course. The primary carrier’s limits of liability, plus the existence of excess coverage, shift the remaining loss and facilitate the loss-spreading that is the principal function of insurance. The excess carrier may further transfer the risk by reinsurance, thus ensuring that no one company bears too much of a single risk. (If it bore too much risk it could not act as a risk-neutral absorber of risks, and insurance would become more expensive.) Each carrier, knowing how much risk it bears and how much it transfers to another, can price its policy reasonably accurately.

It therefore makes sense to treat Western World’s excess clause according to its terms — the clause comes into play whenever the “loss” is covered by another carrier. It would simply confuse things to smuggle clauses meant to deal with moral hazard into the clause meant to apportion payments among carriers.

The complaint filed against the City was based in part on a claim of disparate impact, and therefore the loss was at least presumptively covered by Western Casualty. That Western World also offered primary insurance on a risk (intentional but not wilful discrimination) that Western Casualty found too afflicted with moral hazard is not material unless it turns out that this is the source of a claimant’s loss. But this cannot often be the case; ordinarily it is easier to show disparate impact than to show intentional discrimination. As long as a plaintiff can bring suit under a statute that permits recovery for disparate impact Western Casualty’s policy will cover the “loss.” Western Casualty covered the full loss here; it does not dispute its obligation to indemnify the City. Western World also covered the loss, in the same sense Western Casualty did. Because when a case is settled the claims of the two insurers must be resolved according to the terms of the excess clauses, Western World prevails.

Only one more argument requires comment. Each policy contained a clause requiring the insurer to defend the City. As the district court observed, the obligation to defend is broader than the obligation to indemnify. An insurer is required to defend whenever the loss is even arguably within the policy. E.g., Conway v. Country Casualty Insurance Co., 92 Ill.2d 388, 65 Ill.Dec. 934, 442 N.E.2d 245 (1982). But when one policy is primary and the other is excess, only the primary insurer need defend claims below the limits of the primary policy.

*386 It was possible to tell from the face of the two policies that Western Casualty was required to defend as a primary carrier, because disparate impact was one of the theories of the complaint against the City. As we have construed Western World’s policy, Western Casualty’s coverage of the “loss” made Western World’s obligation that of an excess carrier. It was therefore not required to defend. Had the case gone to judgment against the City, and had that judgment revealed that Western Casualty’s policy did not cover the “loss,” then the principle of Royal Globe might have allowed Western Casualty to recover its costs of defense from Western World. An entitlement to recover ensures that other carriers do not hang back and shirk their obligations when contribution to the defense would reduce the chance of any recovery by the plaintiff. We need consider the possibility no further, however, in light of the fact that Western Casualty was properly in the picture as a primary carrier from beginning to end.

AFFIRMED.