
781 F.Supp. 1289 (1991)
Gilbert PURZE and Jerome Purze, doing business as Park Place Investments Partnership, Plaintiffs,
v.
AMERICAN ALLIANCE INSURANCE COMPANY, Defendant.
No. 90 C 1971.
United States District Court, N.D. Illinois, E.D.
November 27, 1991.
*1290 Jeffrey L. Warnick, Crystal, Heytow, Altieri & Warnick, P.C., Chicago, Ill., for plaintiffs.
Norman C. Nelson, Robbins, Salomon, Wolf, Schlesinger & Miller, Ltd., Chicago, Ill., for defendant.

OPINION
EASTERBROOK, Circuit Judge.[*]
Most of the facts in this diversity action have been stipulated. A bench trial on November 15, 1991, provides the foundation for resolving the remaining disputes. I adopt all of the stipulated facts, repeating them only to the extent necessary for background. This opinion contains the findings of fact and conclusions of law required by Fed.R.Civ.P. 52.

I
In August 1988 Gilbert and Jerome Purze sought a policy of insurance on some of the buildings they hold in the name of Park Place Investments Partnership. The Purze brothers buy buildings at tax sales. After paying the delinquent taxes buyers must wait two years, until the possibility of redemption expires, to obtain a tax deed. Park Place bought the building at 709 West 43d Street in Chicago ("the Building") in this way, obtaining the tax deed shortly before they included this parcel, with 31 others, in their application for insurance. Their agent issued a binder requiring American Alliance Insurance Co. to supply the insurance while it decided whether to accept the risk.
A fire occurred in the Building on August 23, 1988, before American Alliance had completed its underwriting investigation. Arson caused the blaze, which damaged the Building's central core but left the outer walls (and much of the interior) suffering only from smoke and water damage. The loss exceeded the policy limit of $100,000 on the Building, and the Purzes applied to American Alliance for indemnification of this sum plus $6,000 in lost rentals (the policy set a limit of $10,000 in lost business income for this property), less the $1,000 deductible. American Alliance sent Eugene R. LaBelle to investigate. LaBelle, formerly a public prosecutor, has investigated approximately 400 claims on behalf of American Alliance.
An informant identified the two arsonists, low-lifes who frequented the area. LaBelle naturally was interested in the possibility that someone with an interest in the Building had secured their services, directly or indirectly. Sometimes an old building is worth more dead than alive (perhaps the Building would serve best if razed to make way for new construction, or if displaced by a parking lot), and it does not hurt to collect insurance along the way. LaBelle sought information from the Purzes.
The policy contains three clauses requiring insureds to provide American Alliance with information. Part C under "Common Policy Conditions" provides:
We may examine and audit your books and records as they relate to this policy at any time during the policy period and up to three years afterward.
Part 10(g) under "General Provisions" provides:
If requested, the insured will permit the Company to question under oath at such times as may be reasonably required about any matter relating to this insurance or the claim, including the Insured's *1291 books and records. In such event, these answers must be signed.
Part 10(i) adds for good measure that the insured must "cooperate in the investigation or settlement of the claim". These provisions collectively are the "cooperation clause". Still another provision of the policy states that compliance with its requirements is a condition to payment of any claim.
LaBelle interviewed Gilbert Purze on September 27, 1988, Jerome Purze on November 11, and Edward Stawicki, the manager of Park Place Investments, the same day. These interviews were recorded and later transcribed. Each was brief and general; none was under oath. (The Stawicki interview came to 17 pages, Gilbert Purze's to 38 pages, and Jerome Purze's to 83 pages.) LaBelle inquired about the nature of their business, including the procedures for tax sales. In light of these interviews and other information he had received (on which more below), LaBelle wanted to investigate further. American Alliance retained counsel, who in December 1988 sent the Purzes a demand for documents, to be followed by statements under oath in January 1989. The Purzes sent American Alliance copies of the deed to the property and the policy of insurance, but nothing more. (For brevity, I write of communications between "American Alliance" and "the Purzes", although all of these were by and between their lawyers.)
The Purzes had not furnished any other information by February 3, 1989, when American Alliance served them with a comprehensive demand for access to all documents relating to all of their businesses, including telephone and bank records plus tax returns. The Purzes furnished no documents in response to this letter, but in March they authorized three banks to provide American Alliance with information about their financial condition, in order to allay any fears that deteriorating solvency may have driven them to desperate measures. Each letter told the bank to disclose information about "loans, demand deposit accounts and certificates of deposit ... and [the Purzes'] general creditworthiness", but "without minute disclosure of their assets and earnings." A manager of each bank testified that he understood this letter to allow the release of general information (such as: "The Purzes have a net worth in the low seven figures.") but would not permit American Alliance to inspect any document. American Alliance was not interested in vague assurances and never spoke with the banks. LaBelle wanted to see the files, without filtration, so he could draw his own conclusions.
American Alliance demanded that the Purzes appear for examination under oath on April 3. The Purzes did not show up, nor did they produce Stawicki for the examination American Alliance had set for April 4. Later that month American Alliance warned the Purzes that "continued refusal to cooperate with ... policy conditions and our investigation will result in" refusal to pay the claim. In mid-May the Purzes volunteered to take an oath in support of the statements they had given to LaBelle the prior fall and to arrange access to trust records if American Alliance would specify which land trusts it was interested in. The letter concluded: "At this point, it might be appropriate for you to advise the carrier that the insureds will not provide further information other than as indicated in my prior correspondence short of court order."
The message was conveyed, with the predictable result: on May 25, 1989, American Alliance denied the claim on the ground that the Purzes had not satisfied their obligations under the cooperation clause of the policy.
Exactly four months later the Purzes offered to produce all of the documents American Alliance had sought, and to undergo examination, provided American Alliance would waive any defense of non-cooperation. American Alliance was not interested in reopening the matter, let alone waiving its defenses, and declined the offer.
Another four months passed. On January 29, 1990, the Purzes sent American Alliance copies of their tax returns (plus three charge account numbers) and renewed *1292 their offer to supply other information. This time the Purzes volunteered that American Alliance could retain its defenses. In March American Alliance returned the documents, which it had not examined, reiterating that the matter had been closed in May 1989. The Purzes responded with this suit.

II
These facts, almost all stipulated, show that the Purzes did not comply with the cooperation requirement of the policy. (American Alliance's sole defense to payment is lack of cooperation; there is no claim that the Purzes were implicated in the arson, nor could there be. See Harbor Insurance Co. v. Continental Bank Corp., 922 F.2d 357, 362-65 (7th Cir.1990).) The Purzes' principal argument is that they did not have to cooperate, that unless the insurer can establish prejudice from noncompliance they are entitled to the proceeds whether or not they fulfilled their own obligations. American Alliance insists that full compliance is essential and prejudice irrelevant.
Niagara Fire Insurance Co. v. Forehand, 169 Ill. 626, 629, 48 N.E. 830, 831 (1897), supports American Alliance. The court remarked: "Where an insurance policy makes it incumbent on the insured, in the event of a loss, to produce his books or invoices for examination, he must comply with such provision or he cannot recover." The opinion does not suggest that the insurer must establish prejudice from the noncompliance. Horton v. Allstate Insurance Co., 125 Ill.App.3d 1034, 81 Ill.Dec. 584, 467 N.E.2d 284 (1st Dist.1984), reiterates the message, holding that the insurer is entitled to summary judgment when the insured does not comply with a request for documents.
The Purzes rely principally on Piro v. Pekin Insurance Co., 162 Ill.App.3d 225, 113 Ill.Dec. 220, 514 N.E.2d 1231 (5th Dist. 1987), which holds that substantial compliance with a demand for information is enough. The insured, Piro (what a name for an arson case!), authorized his banks to release copies of all banking records, permitted an accountant to inspect his business records on behalf of the insurer, and appeared for examination under oath. He did not turn over tax returns and some other information until after the litigation began, however, contending that the additional information was not relevant. The court found that Piro had been "generally cooperative", 162 Ill.App.3d at 228, 113 Ill. Dec. at 223, 514 N.E.2d at 1234, and held that the sufficiency of this cooperation (and the timeliness of subsequent cooperation) was for the jury. Along the way the court referred approvingly to C-Suzanne Beauty Salon, Ltd. v. General Insurance Co., 574 F.2d 106 (2d Cir.1978), which affirmed the denial of summary judgment under New York law when the insurer showed no prejudice from the shortfall of information. Although Piro did not explicitly say that "prejudice" is important in Illinois, the Purzes ask me to hold that it is.
Piro is hard to reconcile with Horton and Niagara Fire Insurance. "Prejudice" is almost impossible to prove  how would the insurer know which turns the investigation would have taken had more information been produced? Horton and Niagara Fire Insurance put the burden on the insured, who agreed to cooperate. At the same time, it is hard to believe that Illinois requires the insured to produce anything the insurer demands. Could American Alliance have demanded that the Purzes produce love letters from their spouses? Discuss their religious beliefs under oath? Sensibly read, the policy authorizes only questions and demands for information material to the subject. "Materiality" builds in a concept of prejudice  not actual prejudice, but potential prejudice, in the sense that the information (or its absence) could be salient to a proper decision.
Some of American Alliance's demands reach beyond the Purzes' real estate activities into their other businesses and strain if not surpass the limits of materiality. But the Purzes did not limit their objections to demands and questions they deemed immaterial. They objected generally. They did not show up for examination under oath. They did not produce Stawicki for examination *1293 under oath. Until September 1989 they refused to disclose any documents beyond the insurance policy (which of course the insurer had), the deed to the Building, and trust records (which would reveal no more than the holders of beneficial interests  who, the Purzes asserted, were themselves only). Piro was generally cooperative, the Purzes generally uncooperative. Unless almost everything the insurer requested was immaterial, the Purzes failed to satisfy their obligations by May 1989, when American Alliance denied their claim.
Piro holds that the timeliness of disclosure is a question for the trier of fact, and I conclude that the Purzes' offers after May 1989 were untimely. The offer in September 1989 was not bona fide; an offer coupled with a demand that the insurer waive its defenses is the equivalent of no offer. Late January 1990, when the Purzes made a genuine offer to cooperate, was more than 17 months after the fire. LaBelle testified that the trail grows cold in time, and there is a risk that the insureds deferred cooperation until they could purge their files of documents the insurer would find interesting. A cooperation clause implies that the insured must cooperate promptly after the casualty, on the insurer's demand and not at his leisure. I credit LaBelle's testimony that February 1990 was too late for an investigation calculated to produce reliable answers.

III
LaBelle testified that he wanted access to the Purzes' financial and telephone records to investigate potential motives for arson and to find out whether there were calls to or from the persons who set the fire. Access to the records themselves, without the mediation of bank officials, may be important because documents mingled with the financial statements may supply clues, according to LaBelle. As I have said, some of the requests seem excessive, but the requests concerning Park Place and the telephone records are material in the circumstances.
Consider what LaBelle knew or suspected when he made the demands for documents and interviews under oath (I credit LaBelle's testimony in all respects):
 Arson occurred while the coverage was under binder (that is, before American Alliance had an opportunity to evaluate the risk).
 A risk report evaluating six of the thirty-two properties concluded that one is a vacant lot rather than the building described in the application. (This turned out to be a false alarm; the policy lists a building at "1501 E. 71st"; although there is a vacant lot at that address of 71st Street, the Purzes own the building at 1501 E. 71st Place. But LaBelle did not know this.)
 The list of "additional insureds" in the policy includes a number of land trusts, so the real parties in interest may be concealed, and some of these concealed parties may have had something to gain from arson or may have had interests in buildings that experienced other suspicious fires.
 The Purzes' total cost for the Building was approximately $30,000, substantially less than the amount of insurance (which was in turn substantially less than the replacement cost of such a building).
 During his interview in September 1988, Gilbert Purze stated that the Purzes' enterprises had experienced only two trivial fire losses. LaBelle learned from the Metropolitan Chicago Loss Bureau that 17 days before Gilbert Purze made his statement an apartment building the Purzes owned in Elgin, Illinois, had burned down. Three people died; arson was suspected.
 LaBelle heard a rumor that the Purzes had agreed to sell the Building to the owner of a neighboring convenience store, who planned to raze the Building. A fire would produce insurance proceeds without obstructing such a transaction. (I describe this as a "rumor" because the testimony about the sale would be hearsay if offered for *1294 truth, but was admissible when limited to explaining LaBelle's suspicions.)
 The application for insurance indicated that the Building was occupied. So did the Purzes' proof of claim, which sought $6,000 for lost rentals. But both Tom Miller (the investigator for the Chicago Fire Department) and LaBelle found the building apparently unoccupied. The gas and water were off. (A notice plastered on the Building, dated August 11, 1988, promised prompt discontinuation of water.) The tavern on the first floor contained no liquor or other valuable property, the apartments on the upper floors no furniture. Lack of occupancy implies a planned arson  and also calls the veracity of the application and claim into question.[]
 The arsonists had no apparent motive, opening the possibility that they acted for pay.
 The Purzes were exceptionally stingy with information, a reticence that reinforced other suspicions.
All of this gave LaBelle ample reason to inquire further  to seek telephone records and an interview under oath, to request tax returns and bank records. As LaBelle testified, financial records are forthcoming as a matter of course in insurance investigations. Most of the financial requests were standard in the business. Requests for telephone records are less common, but here were justified.
At trial the Purzes testified that their father had taught them to conduct their business privately. Well and good, but there is a curious inconsistency in the assertion of privacy. First they sat down with LaBelle for interviews, then they clammed up and would furnish nothing of value, and finally (after it was too late) they offered to furnish everything. What happened to their sense of privacy between May and September of 1989? Contrast the approach of Mr. Piro, who opened his business records, authorized his banks to disclose everything, and sat for an examination under oath, objecting only when he thought the inquiries too far afield. It may be, as the Purzes say, they they suspected from the scope of the demand for information and the cancellation of the policy (on the ground of an increase in risk) that American Alliance was looking for an excuse not to pay. Such a belief does not explain why, by refusing to cooperate, the Purzes would furnish the excuse American Alliance sought; and if it explains their conduct it nonetheless does not justify it.
If the Purzes had followed Piro's course, producing some documents while balking at the request for others, submitting to examination under oath while objecting to questions at the fringe of relevance, this would be a different case. As things stand, American Alliance had solid reasons to investigate, and the Purzes were basically uncooperative. Their disregard of obligations under the cooperation clause prevents collection on the contract of insurance.
*1295 The clerk will enter judgment for the defendants.
NOTES
[*]   Of the Seventh Circuit, sitting by designation.
[]   As the question at hand is whether LaBelle reasonably requested additional documents and statements from the Purzes, it is not necessary to decide whether the building was actually unoccupied at the time of the fire. Stawicki testified at trial that he found the tavern in operation in early August 1988, before applying for the insurance. Inspector Miller's testimony undermines this but does not exclude the possibility that the tavern and dwellers vacated the building afterward. LaBelle knew, however, that the tavern's Illinois liquor license expired June 30, 1988, and its city license on April 30, 1988. A calendar on the wall of the tavern displayed the month of April 1988. It is a fair inference that Stawicki lied on the stand; at all events LaBelle had ample reason to believe the Building vacant in August 1988. (The Purzes objected to the introduction of the liquor licenses and calendar on the ground that they were not turned over during discovery. I overrule this objection because the Purzes have not identified any request for such documents. Their request for information "connecting Plaintiffs, no matter how remotely, to the fire" does not fill the bill. American Alliance does not believe that the calendar and liquor licenses "connect" the Purzes to the fire; the insurer believes that they call the veracity of the application and claim into question and furnish grounds for inquiry. These documents were used at trial exclusively to undermine Stawicki's credibility. Phraseology such as "no matter how remotely" does not require the party receiving the request to turn over every document in its possession, because any document could have such an effect.)
