MEMORANDUM OPINION

POSNER, Circuit Judge (Sitting by Designation).

This is a suit for breach of contract by Torco Oil Company against Innovative Thermal Corporation (ITC) and two corporations affiliated with ITC — Caldwell Aircraft Trading Company and Charlotte Aircraft Corporation. Federal jurisdiction is based on diversity, and Illinois law governs the substantive issues. A jury awarded Torco damages of $2,554,110 against all three defendants. I postponed entry of judgment until the submission and resolution of the defendants’ post-trial motions, in which they ask for judgment notwithstanding the verdict or, alternatively, for a new trial. I have decided to deny the motions, and have therefore ordered the entry of judgment for the amount awarded by the jury.

H. Jenks Caldwell is a businessman in Charlotte, North Carolina, engaged primarily in the sale of transport aircraft, aircraft engines, and aircraft parts through several closely held corporations (including Caldwell Aircraft and Charlotte Aircraft) of which he is the principal shareholder and dominating presence. Caldwell Aircraft is a wholly owned subsidiary of Charlotte Aircraft. Like many other businessmen, Mr. Caldwell from time to time pursues business ventures on his own.

As a result of changes in the noise regulations of the Federal Aviation Administration, Caldwell found himself (or rather *1447 Caldwell Aircraft) owning eighty aircraft engines that could not be used in aircraft. He cast about for an alternative use. His quest brought him into contact with John Rivera, a businessman interested in “co-generation.” This term refers to techniques for using energy that normally is wasted in the course of producing electricity. Rivera believed that Caldwell’s aircraft engines, which from an engineer’s standpoint are simply gas turbines, could be arranged in a cogeneration network that would enable the engines to produce electricity directly and the energy normally wasted in that process to be used for air conditioning, water purification, or other valuable uses, including the generation of additional electricity. Caldwell and Rivera formed Innovative Thermal Corporation to develop Rivera’s ideas for cogeneration (not limited to finding a use for the aircraft engines). Caldwell contributed $25,000 in cash to the fledgling corporation in return for 50 percent of the stock. Rivera became president of the corporation and the other 50 percent stockholder. He contributed to the corporation — besides his ideas about co-generation, his knowhow, and his time — a fax machine and some computer software of uncertain value. Later, ITC acquired, in exchange for the right to distribute its hypothetical cogeneration systems, a number of control devices called “En Logs.” The evidence showed that in all likelihood they were completely worthless — which was fair enough, since the right to distribute ITC’s cogeneration systems turned out to be worthless, too, because ITC never did succeed in developing or marketing any such system.

As Rivera explored the possibility of interesting municipalities and other large users of electricity in cogeneration networks to be designed and installed by ITC, he discovered that these potential customers demanded long-term contracts for the supply of the fuel (either oil or natural gas) needed for the network’s generation of electricity. Rivera found a small, shaky, and since defunct company in Oklahoma, known as “Portagaz,” which owned some natural-gas leases; and ITC formed a joint venture with Portagaz, called ITC of Oklahoma, Inc., to which the leases were transferred. But Rivera found that he had lined up the supply of gas that he needed for his cogeneration customers before he had any such customers. The question was what to do with the gas that ITC had contracted to buy before the cogeneration business got going.

Enter, providentially, Torco Oil Company, a substantial midwestern distributor of oil and gas, headquartered in Chicago. Torco was in the process of negotiating an agreement to supply LTV Steel Company with natural gas for one year. Torco is a middleman, not a producer; it needed a source for the gas it wanted to sell to LTV. It discovered that ITC both had — or at least said it had — the requisite quantity of gas to sell and wanted to sell it on a short-term basis. On June 22, 1988, ITC and Torco signed the contract that is the nub of this lawsuit. The contract is for a fixed quantity of natural gas at a specified price amounting to roughly $1.1 million a month for the twelve months of the contract. The contract specifies the following “terms of payment”: “Metered payable every thirty days with a documentary letter of credit for sixty days of production.” Torco obtained from its bank a $2.2 million standby letter of credit. ITC claims that it refused to accept the letter of credit, because a standby letter of credit is not a documentary letter of credit; at all events, ITC never shipped any gas. Torco claims that the standby letter did comply with the contract, that ITC didn’t ship the gas because it didn’t have it to ship and hence that ITC — not Torco — broke the contract, and that the objection to the letter of credit was something that Rivera and Caldwell cooked up after ITC’s default in an effort to shift the blame for the breach to Torco. In accordance with section 2-713 of the Uniform Commercial Code, Torco seeks damages based on the difference between the price in its contract with ITC and the market price, which was higher; and it seeks them against Caldwell Aircraft and Charlotte Aircraft as well as against ITC, on the ground that ITC was a mere shell— the alter ego of H. Jenks Caldwell and his *1448 other corporations. ITC’s cogeneration business never got off the ground; it is inactive and assetless; a judgment against it alone would be worthless. The jury bought Torco’s arguments in toto.

At trial a major issue was whether the standby letter of credit complied with the contractual requirement that Torco furnish a “documentary” letter of credit. It is odd that there should not be a standard terminology in these matters, but there isn’t, though the meaning of “standby” letter of credit, at least, is clear. A standby letter of credit, also known as a “guaranty” letter of credit, obligates the bank that issues it to pay the beneficiary (in this case ITC) an amount of money not to exceed the figure specified in the letter ($2.2 million) if the beneficiary submits to the bank documents showing that the applicant for the letter of credit (Torco) owes the money to the beneficiary and has refused to pay it upon proper demand. Thus, if ITC delivered a month’s quantity of gas to Torco at a delivery point specified in the contract and Torco refused to pay the invoice, ITC could go to the issuing bank, present it with the invoice, the record of delivery, and a statement that Torco had refused to pay the invoice in accordance with the terms of the contract, and if the documents seemed in order the bank would have to pay ITC the amount of the invoice. If the letter of credit had been not a “standby” letter but a “commercial” letter of credit, ITC would not have had to submit evidence that Torco had refused to pay the invoice. In fact, it would not have had to bill Torco at all. It could have billed the bank directly. The difference is potentially important because a commercial letter of credit can be used as collateral for a loan, and a standby letter cannot be. ITC says it could have taken a commercial letter of credit to its own bank and obtained, by way of a loan secured by the letter, the money it needed to buy the gas that it had agreed to resell to Torco. A standby letter of credit is no good for these purposes because ITC’s bank could not demand payment simply upon presentation of the invoice and the delivery ticket to Torco’s bank. ITC’s bank would have to demand the money from Torco. Only if and when Torco’s failure to cough it up could be shown to be a default could ITC’s bank turn to Torco’s bank for payment.

It never became fully clear at trial why ITC should have had to buy gas, given its joint venture with Portagaz. Torco’s theory was that Portagaz never did have deliverable gas. Rivera testified that there merely was a delay in hooking up the wells leased by Portagaz (and transferred to the joint venture) to an interstate pipeline, so that he had to get the first two months’ supply of gas from someone else. Why, with Caldwell's excellent credit rating, ITC couldn’t have gotten the necessary credit without having to brandish a commercial letter of credit was never explained. Rivera never did seek bank financing, but — by his own testimony — simply allowed the deal with Torco to collapse when the desired letter of credit was not forthcoming.

ITC argued at trial that “documentary” letter of credit is a synonym for “commercial” letter of credit. Torco riposted that a standby letter is documentary too, because it requires the beneficiary to present documents to the issuing bank, just like a commercial letter — only not so many documents. Each side called an expert witness. ITC’s expert testified that while what are now called commercial letters of credit date back to the early nineteenth century, standby letters of credit are a twentieth-century innovation. Until standby letters came along, all letters of credit were called documentary letters of credit and were unconditional guarantees of payment, usable therefore, and used, as devices for facilitating sales of goods, such as the sale of gas by ITC to Torco in this case. The facilitative function derives from the fact that the seller does not have to depend on the buyer for payment or even have to establish the buyer’s default. Standby letters of credit, the witness testified, are ordinarily used to guarantee performance rather than payment; they thus are much like performance bonds. This witness was a law professor from out of the state, and Torco’s counsel made much of the professor’s lack of practical banking experience and his carpetbagger status, asking darkly *1449 why ITC hadn’t been able to find a Chicagoan to testify about letters of credit. Tor-co’s witness was a Chicago bank officer, whose lack of formal education counsel turned to Torco’s advantage by presenting her to the jury as a model self-made woman. (Such are the absurdities of trial by jury in complex commercial cases.) Professor Byrne’s historical narrative is supported by the scholarly literature. Paul Verkuil, Bank Solvency and Guaranty Letters of Credit, 25 Stan.L.Rev. 716, 717 n. 10, 725 (1973). The “document” in “documentary” is the document of title that the traditional letter of credit requires the seller to tender to the issuing bank, showing that title to the goods has passed to the buyer, the bank’s customer. Id. at 718; John F. Dolan, The Law of Letters of Credit: Commercial and Standby Credits U 2.04, at pp. 2-5 (1984). The opposite of a documentary letter of credit is a clean letter of credit, which requires only a demand for payment without need for additional documentation. Id., 111.07[2], at pp. 1-26 to 1-27; In re Fuel Oil Supply & Terminaling, Inc., 837 F.2d 224, 229 n. 13 (5th Cir.1988). “The standby letter is often clean,” Dolan, supra, 111.07[2], at pp. 1-26, because it may require merely a demand for payment supported by a conclusional statement that the primary obligor has failed to pay. Yet the testimony of Torco’s expert witness that, today anyway, a standby letter of credit is considered a type of documentary letter of credit when, as in this case, it requires the submission of specified documents (beyond the demand itself and accompanying statement of default) as a condition precedent to the bank’s having to honor it, has greater support in the relevant authorities than Byrne’s testimony to the contrary — as Bryne, indeed, had come close to admitting in his deposition. It is consistent with Do-lan’s statement that “the standby letter is often clean.” (Emphasis added.) And compare Uniform Customs and Practices for Documentary Credits, art. I (1983); Apex Oil Co. v. Archem Co., 770 F.2d 1353, 1356 (5th Cir.1985); Ensco Environmental Services, Inc. v. United States, 650 F.Supp. 583, 590 (W.D.Mo.1986); Gunn-Olson-Stordahl Joint Venture v. Early Bank, 748 S.W.2d 316, 319 (Tex.App.1988); and 6B Michie on Banks and Banking, ch. 12, § 28, at p. 117 (1987), with Consolidated Aluminum Corp. v. Bank of Virginia, 544 F.Supp. 386, 393 (D.Md.1982), aff’d, 704 F.2d 136 (4th Cir.1983).

Actually there were two letters of credit in this case. Rivera rejected the first one, which was handed him by Greg Wilkins — who was the head of Torco’s natural gas marketing division and negotiated and signed the contract on Torco’s behalf— upon the signing of the contract; and Wilkins wrote across the letter that it would be revised to be “co-terminus” with the contract, meaning that it would be revised to conform to the terms of the contract. Rivera testified that the key revision was to convert the letter of credit from a standby to a documentary (in the sense of commercial) letter of credit. Wilkins testified that the only revisions Rivera asked for concerned the delivery point for the gas and other immaterial details. Torco went back to its bank and obtained another letter of credit, which changed the delivery point and made the other minor corrections but retained the standby feature. Wilkins sent the new letter of credit to ITC. There was no reply for some weeks, and then ITC announced that Torco had broken the contract. Torco claims that ITC refused to deliver the gas not because it was dissatisfied with the letter of credit but because it could not obtain the gas either from Portagaz, a fly-by-night venture of a former credit manager with no experience in the gas business, or from anyone else. The jury believed Torco, as it was entitled to do; Rivera was not a credible witness.

ITC argues that I should have asked the jury to decide whether there was “a meeting of the minds.” Chicago Litho Plate Graining Co. v. Allstate Can Co., 838 F.2d 927, 930 (7th Cir.1988); Midland Hotel Corp. v. Reuben H. Donnelley Corp., 118 Ill.2d 306, 313-14, 113 Ill.Dec. 252, 256, 515 N.E.2d 61, 65 (1987). The argument was waived by not having been raised in timely fashion. In so concluding, I reject ITC’s argument that surprise testimony at the *1450 trial injected the issue into the case unexpectedly and thus excused the earlier waiver. The surprise testimony, by Wilkins and by Torco’s financial officer, Crowe, who had obtained the letters of credit, suggested the possibility (no more than that) that Crowe in asking the bank for a standby letter of credit had been relying on an earlier version of the contract, which had referred to the letter of credit as a standby letter of credit, rather than the later, signed version, which referred to it as a documentary letter of credit. But if this is what happened, it would not show that the parties had meant different things by “documentary letter of credit”—in which event, conceivably, there would have been so profound a misunderstanding, not chargeable to the negligence of either party, that the contract would have been unenforceable, as in the famous case of Raffles v. Wichelhaus, H. & C. 906, 159 Eng.Rep. 375 (1864), discussed in 2 E. Allan Farnsworth, Farns-worth on Contracts § 7.9 (1990). It would show only that Torco, by virtue of Crowe’s reading the wrong document, had broken the contract after it was signed.

So the objection to not giving the instruction was waived. It has in any event no merit. It is of course possible that Torco thought “documentary” letter of credit included “standby” letter of credit and that ITC thought it excluded it. But the entire thrust of ITC’s case was to the contrary. Rivera testified emphatically that he told Wilkins that a standby letter of credit did not comply with the contract and that Wilkins agreed, implying a meeting of the minds and a breach by Torco. Of course the jury could disbelieve Rivera. Undoubtedly it did. But the jury could not disbelieve Rivera and find in favor of ITC, for Rivera was the key witness for ITC concerning the negotiation of the contract. A rational jury that disbelieved Rivera was bound to believe Wilkins, who testified that Rivera had no complaint about the standby feature in the letter of credit that Wilkins tendered to him.

So there was a breach by ITC, and there is no challenge to the calculation of damages. The remaining question concerns the piercing of ITC’s corporate veil to reach the assets of other corporations controlled by H. Jenks Caldwell. The defendants do not complain about the instruction, which followed closely their own submission, but they argue that Torco failed to present evidence from which a reasonable jury could infer that Illinois’ test for piercing the corporate veil had been satisfied. That test, the parties agree, is accurately stated in Van Dorn Co. v. Future Chemical & Oil Corp., 753 F.2d 565 (7th Cir.1985); see also Koch Refining v. Farmers Union Central Exchange, Inc., 831 F.2d 1339, 1345 (7th Cir.1987). It has two parts. The party seeking to pierce the corporate veil must show first that there has been abuse of the corporate form such that one corporation has been made a “mere instrumentality” of the other (the “other” could of course be an individual rather than another corporation), as evidenced by such conduct as “(1) the failure to maintain adequate corporate records or to comply with corporate formalities, (2) the commingling of funds or assets, (3) undercapitalization, and (4) one corporation treating the assets of another corporation as its own,” and second that “adherence to the fiction of separate corporate existence would sanction a fraud or promote injustice.” Id. at 570.

The first part of the test clearly is satisfied here. ITC maintained few, possibly no, corporate records, and complied with no (other) corporate formalities. The expenses of ITC, amounting to some $140,-000 over its brief active life, were paid entirely by Caldwell Aircraft and Charlotte Aircraft. ITC had essentially no capital—it is not even clear that Caldwell’s $25,000 contribution was ever actually made. ITC was not undercapitalized; it was uneapital-ized. The only corporate records produced at trial were ledger books which purported to record all the cash transfers from Caldwell Aircraft and Charlotte Aircraft to ITC as either loans or contributions to capital— and there was evidence (not much, but enough for the jury to go on) that all these records had been created at one sitting, after the lawsuit began, in an effort to *1451 strengthen the defendants’ litigating position.

But the second part of the Van Dorn test is as important as the first. The conditions I have described are, after all, typical of start-up companies. They often are scantily capitalized. Their staffs are small and do not have time for elaborate bookkeeping and minute-keeping. ITC had only one employee — Rivera. He worked out of his home. It was natural if somewhat irregular for Caldwell to finance the operations of the fledgling enterprise out of the assets of his other corporations without creating a meticulous paper record of inter-corporate transfers. You can get into trouble with the Internal Revenue Service for such casualness, United States v. Mews, 923 F.2d 67 (7th Cir.1991), but it would be an undue burden on entrepreneurship to decree a forfeiture of the invaluable privilege of limited liability, without which much entrepreneurship would be too risky to undertake, merely for what the law of Illinois is pleased to describe as abuse of the corporate form but recognizes is not alone a sufficient basis for such a forfeiture. So I must go on and consider the meaning of the second half of the test, the “fraud or injustice” requirement.

When the creditor seeking to pierce the corporate veil is a tort creditor, that is, an involuntary creditor, the court is faced with the difficult problem of balancing the interest in facilitating risk-taking by allowing entrepreneurs to limit their liability with the interest in preventing enterprises from externalizing the costs of their activities. The clash of values is less acute in a case, such as this, where the creditor (Torco) is a voluntary one, a contract creditor. If you decide to risk selling to or (as here) buying from a corporation that may not have sufficient assets to satisfy a claim arising from its breach of the sales contract, you can hardly complain if the risk materializes and your judgment against the other party cannot be satisfied. On the other hand, if the other party, or persons associated with it, deceive you into thinking that you are dealing with a substantial enterprise, and not a mere shell, then the fiction of separate corporate existence does become an engine of fraud, and you can pierce the veil. Since fraud is independently actionable, one may question the need for a doctrine of piercing the corporate veil in contract cases. But that is a question for the courts of Illinois. For present purposes it is enough to note that if there was evidence from which a reasonable jury could infer that the defendants and their agents engaged in a scheme to defraud Torco concerning the substantiality of ITC, the Van Dorn test was satisfied and the motion for judgment notwithstanding the verdict must be denied. Satisfied, indeed, in spades, since Van Dorn emphasized that the test is “either the sanctioning of a fraud (intentional wrongdoing) or the promotion of injustice.” 753 F.2d at 570 (emphasis in original). See also Koch Refining v. Farmers Union Central Exchange, Inc., supra, 831 F.2d at 1345. I am not myself happy with this formulation, and hope it is not a canonical statement of the Illinois position, because it places limited liability too much at the mercy of juries. In this case, though, there was evidence of intent to defraud.

Granted, it’s a close call. Torco asked Rivera for financial information concerning ITC. Rivera responded with nothing about ITC, but instead with financial statements of Caldwell Aircraft and Charlotte Aircraft. Torco asked for a bank reference for ITC and Rivera gave it the bank where H. Jenks Caldwell and his corporations, but not ITC, do their banking. I permitted over the defendants’ vigorous objection testimony concerning an abortive deal between ITC and another company in which Rivera furnished the other company with a document that could be read to imply that the Caldwell corporations were backers or guarantors of ITC. I allowed in this evidence to establish a pattern of fraudulent dealing by Rivera, acting on behalf of Caldwell and his corporations. Fed.R.Evid. 404(b). Torco naturally was interested in the financial solidity of the firm with which it was about to sign a multimillion dollar contract upon which Torco’s ability to comply with its own multimillion dollar contract, with LTV, hinged. Torco was in fact sued by LTV when the ITC contract fell *1452 through, and settled for a substantial sum. Little did Torco know it was dealing with a company that, at the time, had one employee, no office except that employee’s home, no experience in the business in which it was engaging, zero assets, and a negative net worth because it owed money to Caldwell Aircraft and Charlotte Aircraft. Maybe Torco should have done more to investigate the financial condition of its contract partner, but a reasonable jury could infer from the conduct of Rivera in response to Torco’s request for financial information that the defendants deliberately created an appearance either that ITC was a firm commensurate in financial responsibility with Caldwell Aircraft and Charlotte Aircraft or that those corporations were guaranteeing ITC’s ability to finance the purchase of gas necessary to honor its contract to sell gas to Torco. If there was fraud, Torco’s contributory negligence would not be a defense, A M-PAT/Midwest, Inc. v. Illinois Tool Works Inc., 896 F.2d 1035, 1041 (7th Cir.1990), and piercing the corporate veil and reaching the assets of those corporations would be, as the jury found, an appropriate remedy.

The defendants did not and do not argue that the “fraud or injustice” that must be shown to pierce the corporate veil must be proved by clear and convincing evidence. As I have said, maybe the separate doctrine of piercing the veil should be dropped in contract cases and the prevention of the sort of misconduct alleged in this case left to the common law of fraud, and in that event Torco might lose because I do not think it proved fraud by clear and convincing evidence. But that is a decision for the Illinois courts, not the federal courts, to make.

The defendants’ motions are denied, and final judgment for the plaintiff will be entered in accordance with the jury’s verdict.