EASTERBROOK, Circuit Judge.

The Chicago Flood of 1992 occurred when the Chicago River sprung a leak and drained into a tunnel system connecting many buildings in the Loop. Events were set in motion in August and September 1991, when Great Lakes Dredge Dock Co. replaced the pilings ("dolphins") protecting the Kinzie Street Bridge. Because of Great Lakes' carelessness, poor maps or other directions provided by the City, or a combination of events, Great Lakes drove dolphins into the riverbed immediately above one of the tunnels that had been built almost a century earlier to move coal and other freight without tying up the City's streets. Buildings in Chicago no longer burn coal, but the old tunnels have found new uses, such as carrying chilled water for air conditioning or hosting electric power and communications lines. Cracks in the ceiling of the tunnel, caused by the work in the River, grew as the weeks passed. Deterioration could have been stopped if the damage had been detected during inspections and the roof shored up pending repairs, but this did not happen. On April 13, 1992, the roof caved in and the waters of the Chicago River rushed through the tunnel system, flooding basements and streets throughout downtown Chicago. Damage has been estimated at more than $300 million (and by some accounts more than $1.5 billion). Navigation on the River was halted for about a month while the tunnel was repaired. Jerome B. Grubart, Inc. v. Great Lakes Dredge Dock Co., 513 U.S. 527, 115 S.Ct. 1043, 130 L.Ed.2d 1024 (1995), affirming 3 F.3d 225 (7th Cir. 1993), holds that Great Lakes' request for limitation of liability under 46 U.S.C. §§ 181-96 comes within the admiralty jurisdiction. Our case concerns not the amount of liability but the allocation of responsibility among Great Lakes' insurers. As part of a settlement the City of Chicago and a class of injured parties have succeeded to Great Lakes' rights under the policies, but for clarity we refer to Great Lakes as the insured.

Insurance coverage could have been simple. Great Lakes acquires insurance to match its fiscal year, from August through July. Both the damage to the tunnel and the flood occurred during one policy year. At the beginning of August 1991 Great Lakes was the beneficiary of three relevant policies: a primary policy with a cap of $1 million and two excess policies purchased by its corporate parent Itel Corporation, and on which Great Lakes was an additional insured: a first excess policy providing $40 million in coverage, and a second excess policy providing $60 million in additional coverage. Both of these excess policies were underwritten by a consortium that for convenience we call the "London Insurers." (Details about the participants would have been relevant and likely would have led to dismissal if jurisdiction depended on diversity of citizenship, see Indiana Gas Co. v. Home Insurance Co., 141 F.3d 314 (7th Cir. 1998), but admiralty jurisdiction saved the day.) Things grew complicated when Itel sold its subsidiary to the Blackstone Dredging Partnership L.P. on October 15, 1991 — after the damage to the roof of the tunnel, but before the flood. The spinoff made it impossible for Great Lakes to remain as an additional insured on Itel's policies. So as part of the transaction Itel and Blackstone arranged for Great Lakes to be deleted as an insured on the first excess policy; the London Insurers then wrote an identical $40 million policy naming Blackstone as the insured and Great Lakes as an additional insured, charging exactly the premium that had been refunded to Itel for the cancellation of the remaining term on the original policy. The $60 million second-tier excess policy was canceled, but Blackstone purchased a $10 million second-tier excess policy from Continental Insurance. Thus when the damage to the tunnel's roof occurred, Great Lakes had $100 million worth of excess coverage, all through the London Insurers; when the roof collapsed, Great Lakes had only $50 million in coverage, of which $40 million was supplied by the London Insurers and $10 million by Continental. (The parties call the policies in force when the dolphins were driven the "first-period policies" and the policies in force when the flood occurred the "second-period policies." We follow suit.)

The change in both the identity of the underwriters and the maximum coverage between the first and second periods has led to conflict. Continental contended in the district court that the first-period policies supply all of the coverage, because that is when Great Lakes weakened the tunnel's roof. The London Insurers, by contrast, contended that only the second-period policies were triggered, because they were in force when the flood occurred. (They concede that the first-period policies cover damage to the tunnel itself, but this loss is trivial compared with the damage sustained by businesses whose basements were flooded and by the utilities that had laid cables in the tunnels.) Great Lakes contends that all excess policies were triggered and should be stacked — that the maximum indemnity is not the $50 million or $100 million Great Lakes had in force at any one time, but $150 million, the sum of all policy limits in force in either period. The district court agreed with Great Lakes, issuing a declaratory judgment that the London Insurers must pay up to $140 million and Continental up to $10 million, no matter who suffered each loss and no matter when the losses occurred. The judge added that all insurers must pay prejudgment interest and that the London Insurers must pay a penalty of almost $1 million for bad faith in delaying recognition that Chicago was an additional insured on the $1 million primary policy. See 57 F.Supp.2d 525 (N.D.Ill. 1999) (principal ruling); 1999 U.S. Dist. Lexis 13914, 1999 WL 705599 (Aug. 25, 1999) (order resolving remaining issues); 1999 U.S. Dist. Lexis 16296, 1999 WL 966472 (Sept. 28, 1999) (declaratory judgment).

Only one of the policies was written out in full, but the parties agree that its language is universally applicable. Thus all policies cover property damage caused by an "occurrence," a term defined as:

an accident or a happening or event or a continuous or repeated exposure to conditions which unintentionally results in . . . Property Damage . . . during the policy period. All such exposure to substantially the same general conditions existing at or emanating from one premises or location shall be deemed one Occurrence.

The district court concluded that both the damage to the tunnel structure and the losses from flood waters are occurrences under this definition. While this case was being litigated in the district court the parties agreed that Illinois law supplies the rule of decision; the London Insurers have changed their tune on appeal, arguing that federal law governs in an admiralty action. See Continental Casualty Co. v. Anderson Excavating Wrecking Co., 189 F.3d 512 (7th Cir. 1999) (applying federal law to an insurance dispute in admiralty). That new line of argument has been met by a claim of forfeiture. To simplify analysis we follow the parties' original agreement, though with some sidelong glances at admiralty law. See Kamen v. Kemper Financial Services, Inc., 500 U.S. 90, 100 n. 5, 111 S.Ct. 1711, 114 L.Ed.2d 152 (1991) (courts are entitled, though not required, to apply a body of law chosen by the parties even if this is not the law the court would choose on its own).

The district judge rejected as unsupported by either the policies' language or Illinois case law the London Insurers' contention that only a person who suffers injury while the policies are in effect may resort to those policies. This was the principal ground on which the London Insurers sought to restrict coverage of the first-period policies to the cost of repairing the tunnel. Having concluded that all of the policies apply to all injuries, the district judge then stacked the coverage limits on two grounds: first, this is what Zurich Insurance Co. v. Raymark Industries, Inc., 118 Ill.2d 23, 112 Ill.Dec. 684, 514 N.E.2d 150 (1987), did in an asbestosis case; second, the policies omit an anti-stacking clause found in a standard form prepared by Lloyd's of London. Both the London Insurers and Continental have appealed. Continental no longer argues that all liability must be borne by the London Insurers, but it does oppose stacking and prejudgment interest. The London Insurers object to stacking, to the use of the first-period policies to cover flood losses, to prejudgment interest, and to the bad-faith penalty. (A third appeal, No. 00-4295, concerns the district judge's costs award. We stayed briefing on this appeal because costs must be reconsidered in light of our disposition of the merits.) We start with stacking.

1. Stacking. Great Lakes argues, and the district court held, that it can pick any policy during either period and require its insurer to bear the whole loss up to the limit of liability. If this does not cover the loss, the insured names a second policy, and so on until all have been exhausted. The strategy is known variously as "stacking" and "joint and several liability" (an unusual use of that phrase, but one entrenched in insurance decisions). See Olin Corp. v. Insurance Co. of North America, 221 F.3d 307, 322-24 (2d Cir. 2000). See also Comment, Allocating Progressive Injury Liability Among Successive Insurance Policies, 64 U. Chi. L. Rev. 257 (1997). A recent decision by this court concludes that stacking is not an appropriate response to a single tort that spans multiple policy periods. See Sybron Transition Corp. v. Security Insurance, 258 F.3d 595 (7th Cir. 2001). That would be clear enough if, for example, the tunnel had collapsed before Great Lakes finished driving the dolphins. All responsibility would be under the policies then in force; that Great Lakes acquired a new corporate parent in October, and a new set of insurers, would not require those insurers to pay just because some of the victims of the tort had continuing losses, or because the losses could not be quantified until the new policy period. One occurrence, one policy. That's what the definitional clause says. Why should things be otherwise because the piles were driven in the first period and the roof caved in during the second? In either case Great Lakes committed a single tort, with the same injury. So following the approach of Sybron (and Olin, which Sybron followed) is incompatible with stacking. But both Olin and Sybron applied New York law; perhaps Illinois law is different.

Relying on Zurich Insurance, the district court concluded that Illinois is different. Zurich Insurance rejected the position taken by some courts that the sole trigger for coverage in occupational-disease cases occurs when the disease becomes manifest. Instead, the Supreme Court of Illinois held, the policies in force when asbestos is inhaled and when the disease becomes manifest are available for indemnity. The opinion went on to say that the limits of each policy are available, from which the district court inferred that Illinois has adopted joint and several liability. But Zurich Insurance interpreted the language of particular policies; the Supreme Court of Illinois did not establish a principle that transcends the text of insurance contracts. At least two appellate decisions in Illinois since Zurich Insurance have concluded that the Supreme Court of Illinois does not require joint and several liability independent of policies' language. See Missouri Pacific R.R. v. International Insurance Co., 288 Ill.App.3d 69, 223 Ill. Dec. 350, 679 N.E.2d 801 (1997); Outboard Marine Corp. v. Liberty Mutual Insurance Co., 283 Ill.App.3d 630, 219 Ill.Dec. 62, 670 N.E.2d 740 (1996). See also Roman Catholic Diocese of Joliet, Inc. v. Interstate Fire Insurance Co., 292 Ill. App.3d 447, 456, 226 Ill.Dec. 477, 685 N.E.2d 932, 939 (1997). Like the intermediate appellate courts in Missouri Pacific and Outboard Marine, we think it likely that, when squarely faced with the question, the Supreme Court of Illinois will follow the better reasoned (and more numerous) decisions of other jurisdictions that make policies' language the benchmark for stacking. See not only Olin (representing New York law) but also, e.g., Public Service Co. of Colorado v. Wallis Cos., 986 P.2d 924, 939-40 (Colo. 1999); Northern States Power Co. v. Fidelity Casualty Co., 523 N.W.2d 657, 662-64 (Minn. 1994); Owens-Illinois Inc. v. United Insurance Co., 138 N.J. 437, 650 A.2d 974, 985-96 (1994); Sharon Steel Corp. v. Aetna Casualty Surety Co., 931 P.2d 127, 140-42 (Utah 1997); Gulf Chemical Metallurgical Corp. v. Associated Metals Minerals Corp., 1 F.3d 365, 371-72 (5th Cir. 1993); Commercial Union Insurance Co. v. Sepco Corp., 918 F.2d 920, 923-25 (11th Cir. 1990). (We add, for completeness, that if maritime rather than state law supplies the rule of decision, we would hold, for reasons given in Olin and Sybron, that stacking is inappropriate unless the policies provide for cumulation.)

Great Lakes does not rely on any language in the London Insurers' or Continental policies. Instead it observes that the insurers could have put explicit anti-stacking language in their policies. The absence of such language implies, Great Lakes insists, that cumulation of policy limits is a coverage paid for by the premium. Maybe so, although it is familiar in both contractual and legislative drafting that people over-write, guarding against a misreading with a plenitude of negations; then the absence of one possible negation is a poor reason to conclude that the text has any particular meaning. Instead of seeking to draw inferences from missing language, we use more valuable clues. Recall that the premium for the $40 million policy did not change when Blackstone replaced Itel as Great Lakes' parent corporation. Yet if the division of the original policy into two on October 15, 1991 (the date of its spinoff from Itel) raised the effective policy limit for the 1991-92 fiscal year to $80 million, surely an additional premium would have been charged. There ain't no such thing as a free lunch, even in the insurance business. Great Lakes never carried more than $101 million of coverage at any moment, and in connection with the spinoff it cut that maximum to $51 million. Yet, if stacking is allowed, coverage went from $101 million on October 14 to $151 million on October 16, even though the premium reflected a reduction to $51 million. That is exceedingly unlikely. The parties' transactions thus demonstrate that there is only one limit for the 1991-92 policy year, even though the corporate reorganization led to the creation of two policies, each in force for a shorter period. This conclusion also respects the language of the policies. They do not use the text from the 1971 model form, but they do say: "All such exposure to substantially the same general conditions existing at or emanating from one premises or location shall be deemed one Occurrence." This means that the whole loss from the tunnel collapse is "one Occurrence" even if parts of the injury were felt in two policy periods. Thus it remains only to determine which period is the right one.

2. Trigger and allocation. The $1 million policy was in force the entire year, as was a $40 million first-excess policy (so for this policy it is unnecessary to determine whether the trigger falls in the first period or the second). Continental no longer contests the district court's conclusion that its $10 million second-excess policy was triggered by the collapse, so Continental must indemnify Great Lakes for any loss in the $41 million to $51 million band. (The portion of the district court's judgment providing that an excess policy, once triggered, is available from the first dollar of loss, is untenable; Continental need not pay until the underlying limits have been exhausted.)

The only remaining question about triggering and allocation is whether the London Insurers' $60 million first-period, second-excess policy is available. In principle the answer could be yes; Chicago suffered a loss when its tunnel was damaged while the first-period policies were in force. But no one thinks that it would have cost more than $41 million (or even more than $1 million) to repair the tunnel, and the second-excess policy does not come into play until all underlying policies have been exhausted. This makes it impossible to see how the second-excess policy that ended on October 15, 1991, could have been triggered, unless the future claims of businesses harmed by the flood are projected back into the policy period. Yet in Illinois, as elsewhere, an occurrence policy is not triggered unless loss to the claimant happened while that policy was in force. E.g., Pekin Insurance Co. v. Janes Addems Chevrolet, Inc., 263 Ill. App.3d 399, 200 Ill.Dec. 843, 636 N.E.2d 34 (1994); Seegers Grain Co. v. Kansas City Millwright Co., 230 Ill.App.3d 565, 172 Ill. Dec. 50, 595 N.E.2d 113 (1992); Great American Insurance Co. v. Tinley Park Recreation Commission, 124 Ill.App.2d 19, 259 N.E.2d 867 (1970). This is exactly what the policy itself provides, in direct language, by defining "property damage" as an "accident or happening or event [that] . . . results in a . . . physical injury to . . . tangible property . . . during the policy period" (emphasis added). No loss to businesses in the Loop occurred until April 1992.

Great Lakes relies on cases such as Zurich Insurance that address occupational diseases, pollution, products liability, or other events characterized by long delay between the wrongful act and the manifestation of harm. In cases of this kind, Zurich Insurance held, policies in force at the time of the wrongful acts, in addition to those in force while the harm occurred and became manifest, may be triggered. See also Eljer Manufacturing, Inc. v. Liberty Mutual Insurance Co., 972 F.2d 805 (7th Cir. 1992). The extent to which the Supreme Court of Illinois subscribes to this principle has been called into question by Travelers Insurance Co. v. Eljer Manufacturing, Inc., ___ N.E.2d ___, 2000 Ill. Lexis 1712, 2000 WL 1763322 (Ill. Dec. 1, 2000), which held (in circumstances identical to our Eljer decision) that the installation of a defective product does not trigger coverage until the harm from the defect comes to pass. But the extent to which the Supreme Court of Illinois subscribes to its own opinion in Eljer (and thus disagrees with our Eljer holding from 1992) has been called into question by the grant of rehearing in that case. See 2001 Ill. Lexis 231 (Jan. 29, 2001). Eljer has been rebriefed and reargued in the Supreme Court of Illinois, and until a fresh decision is released state insurance law is up in the air.

Waiting for that decision is unnecessary, however, because the cases such as Zurich Insurance and our opinion in Eljer involve damage to the same property over multiple periods. Here the injured persons are distinct: the City suffered injury when the dolphins were driven into the tunnel's ceiling during the first period, and businesses (as well as the City) were injured when the ceiling collapsed and the flood occurred during the second period. The definitions in the policies show that the businesses did not suffer property damage, and so there was no "occurrence" triggering coverage, until the collapse in April 1992.

What is more, even after the damage to the tunnel, the loss was preventable. Our problem is not at all like asbestosis, where once fibers accumulate in the lung there is nothing to do but wait and see whether disease develops. Here there was a cure: inspection and repair. That is to say, even after the pile driving there was still an insurable event: whether a collapse would occur before the City detected the damage and repaired the tunnel. Not until the second period did the City fail to take precautions that could have avoided all loss to businesses. In February 1992 (while the second-period policies were in force) inspectors discovered a foot of water in the tunnel and saw cracks in its ceiling, yet failed to take steps that would have prevented the roof's collapse. See In re Chicago Flood Litigation, 308 Ill.App.3d 314, 320-21, 241 Ill.Dec. 714, 719 N.E.2d 1117, 1122 (1999). Hence the "occurrence" is in the second period so far as the victims of the flood are concerned. The London Insurers' $60 million second-excess policy therefore has not been triggered.

3. Prejudgment interest. The district court made the London Insurers and Continental jointly and severally liable for more than $2 million in prejudgment interest for delay in funding an $11 million settlement that Great Lakes reached with the City and some of the injured businesses. Our ruling on the stacking question requires revision of that decision in part: Continental cannot be held jointly and severally liable. Moreover, because Continental's policy does not come into play until the underlying limits of $41 million have been exhausted, Continental is not obliged to fund any of this settlement and cannot be required to pay interest for delay. The London Insurers' $40 million first-excess policy was triggered, however, and the London Insurers do not dispute that they tarried in providing indemnity.

Both the district court and the parties have treated prejudgment interest as a matter to be resolved under admiralty law. (They do not remark the inconsistency of this approach with their resort to Illinois law to determine other issues.) Prejudgment interest is an aspect of full compensation and therefore is available under admiralty law; neither equitable considerations nor the existence of a bona fide dispute about liability affect the running of interest. See City of Milwaukee v. Cement Division of National Gypsum Co., 515 U.S. 189, 195, 115 S.Ct. 2091, 132 L.Ed.2d 148 (1995); In re Oil Spill by the Amoco Cadiz, 954 F.2d 1279, 1331-32 (7th Cir. 1992). See also, e.g., West Virginia v. United States, 479 U.S. 305, 310-11 n. 2, 107 S.Ct. 702, 93 L.Ed.2d 639 (1987); General Motors Corp. v. Devex Corp., 461 U.S. 648, 655 n. 10, 103 S.Ct. 2058, 76 L.Ed.2d 211 (1983). The award of interest for the delay in funding the settlement therefore is unexceptionable.

Part of the award, however, reflects not delay in funding the settlement but delay in handing over the entire limits of the $40 million first-excess policy after Great Lakes assigned its rights under this policy to Chicago and a class of injured parties. It is not clear to us why the assignment created any obligation to pay; an underlying loss still must be established. This aspect of the district judge's decision seems to have been influenced by her assignment of joint and several liability; with stacking out of the case the matter of interest on amounts other than the settlement needs a fresh look. Nor is it clear that interest has been adequately separated from the losses. (If, for example, compensation for the time value of money is built into a victim's claim for damages, a separate award of prejudgment interest would be double counting.) So although we agree with the district court that admiralty's norm of prejudgment interest should be applied, we remand for a recalculation that is limited to eligible amounts under the $40 million first-excess policy and does not include any interest against Continental.

4. Bad-faith penalty. The primary $1 million policy had a separate limit of $1 million for legal expenses incurred in defense of claims made against the insured. The London Insurers disbursed the policy limit of indemnity and expended the full $1 million in legal costs on behalf of Great Lakes. Nonetheless, the district judge ordered the London Insurers to pony up an extra $500,000 in indemnity and an additional $495,000 in defense outlays as penalties for bad-faith failure to treat Chicago as an additional insured — which it was, by virtue of its contract with Great Lakes and a clause in the policy promising indemnity to Great Lakes' customers. The London Insurers did not tarry in recognizing their obligation to defend and indemnify Great Lakes, but recognizing the obligation to Chicago, which was not named on the face of the policy, took additional time. Because the London Insurers paid out the policy limits on behalf of Great Lakes, Chicago received none of the benefit even though it was an insured. By requiring the London Insurers to provide an extra $500,000 in indemnity and (almost) $500,000 in defense expenses, the district court sought to put Chicago in the position it would have occupied had the London Insurers recognized that under this policy they owed to Chicago the same duties they owed to Great Lakes.

The London Insurers' principal response on appeal is that the two-year delay in responding to Chicago's demands for indemnity and defense should be chalked up to a series of bureaucratic errors and miscommunication among its brokers and lawyers. Illinois authorizes penalties for bad-faith refusals and delays by insurers, see 215 ILCS 5/155 (a provision authorizing awards of attorneys' fees), but negligence cannot be treated as "bad faith," the London Insurers insist. Like the district court, we find it difficult to see how the problem can be ascribed entirely to paperwork problems. The London Insurers did not disburse the policy limits until April 1995, well after they had recognized that Chicago is an additional insured. Cases such as Travelers Indemnity Co. v. Citgo Petroleum Corp., 166 F.3d 761, 764 (5th Cir. 1999), which hold that it is not bad faith to pay the policy limits on behalf of one insured if no claim has been made by or against another, therefore do not help the London Insurers. See Western Alliance Insurance Co. v. Northern Insurance Co., 176 F.3d 825, 828 (5th Cir. 1999). More to the point, however — for neither of the fifth circuit's cases rests on Illinois law — is the fact that Illinois does not use "bad faith" to describe an insurer's state of mind or to distinguish between negligent and intentional wrongdoing. It is just a label applied to objectively unreasonable conduct that injures an insured — which is to say, negligence. See Transport Insurance Co. v. Post Express Co., 138 F.3d 1189, 1192 (7th Cir. 1998) (Illinois law); Twin City Fire Insurance Co. v. Country Mutual Insurance Co., 23 F.3d 1175 (7th Cir. 1994) (Illinois law); Adduci v. Vigilant Insurance Co., 98 Ill.App.3d 472, 475, 53 Ill.Dec. 854, 424 N.E.2d 645, 648 (1981); Kavanaugh v. Interstate Fire Casualty Co., 35 Ill.App.3d 350, 356, 342 N.E.2d 116, 120 (1975). Illinois courts have adopted a confusing label for a familiar concept, one that lacks any requirement of scienter.

Appellate review of a bad-faith finding is deferential. See Venture Associates Corp. v. Zenith Data Systems Corp., 96 F.3d 275, 280 (7th Cir. 1996); PSI Energy, Inc. v. Exxon Coal USA, Inc., 17 F.3d 969, 973 (7th Cir. 1994). We do not think that the district court committed a clear error or abused its discretion. It is of course hard to know what sanction is appropriate; the London Insurers ask how the district court could be sure that Chicago would have obtained the benefit of $500,000 in indemnity and $495,000 in legal expenses had they discharged their duties. It is a good question; other numbers would have been possible. But the difficulty of reconstructing how things would have gone in an alternate reality is a principal reason why appellate courts accept reasoned resolutions by triers of fact, and because the district judge's split-the-limits approach is a sensible one — the claims made by third parties against Chicago greatly exceed $500,000, so it could have used the indemnity — we affirm this aspect of the judgment except to the extent the district judge added $345,287 in prejudgment interest to the award of $495,000 in legal expenses. As with the award of interest on the settlement, it is unclear whether the district judge properly separated interest from loss. If the $495,000 already includes compensation for the time value of money, there is no basis for prejudgment interest too.

This opinion requires revisions to many aspects of the district court's decision and reconsideration of one aspect of the prejudgment-interest dispute. Proceedings on remand will affect the award of costs, so we do not discuss appeal No. 00-4295 but remand that subject, too, for adjustment as appropriate.

The judgment of the district court with respect to penalties under the primary policy is affirmed. The judgment and the award of costs are otherwise vacated, and the case is remanded for further proceedings consistent with this opinion.