POSNER, Circuit Judge.

David Chase brought this diversity suit against Consolidated Foods Corporation, claiming that Consolidated had broken its contract with Chase to sell him the Fuller Brush Company, a division of Consoldiated. The jury gave judgment for Consolidated, and Chase appeals, claiming error in the instructions to the jury and in exclusion of evidence. The parties agree that Illinois law governs the substantive issues.

The alleged error in the instructions relates to the apparent authority of Newman, who was Consolidated’s vice-president, secretary, and general counsel. Newman drafted an agreement for Chase to buy the Fuller Brush Company. Described as a letter of intent and signed by both parties (in June 1975), the agreement was expressly subject to the parties’ negotiating a “definitive agreement” and to approval by Consolidated’s board of directors. The agreement also allowed Chase to cancel it *568 after studying the company — and in October he did cancel it. But negotiations resumed, and Newman prepared a new agreement in the form of a letter to Chase that began, “This is to confirm our understanding of the salient economic terms of your offer to acquire” Fuller Brush. The parties signed this agreement on November 17, 1975. It left a number of issues to subsequent negotiations — notably, determining the size of Fuller Brush’s unfunded pension liability that the purchaser would assume — and did not specify a closing date for the sale.

Both agreements contain a formula for determining the purchase price of the Fuller Brush Company, although the record is not sufficient to enable us to compute an actual purchase price from the formula. What is clear, however, is that the November 17 agreement required Chase to put up $5 million in cash toward the total price. He wanted to borrow this money, and he thought that any lender would want to know whether Consolidated’s board of directors had approved the sale. On November 26, at the request of Chase’s associate, Calabro, Newman sent a telegram to Chase stating: “The Board of Directors of Consolidated Foods Corporation ratified the approval of the Executive Committee’s agreement to sell the Fuller Brush Company to you based upon the terms outlined in the letter of November 17, 1975.” But the board had not approved an agreement to sell; on November 26 it had approved the November 17 agreement only as a basis for further negotiations.

After November 26, relations between the parties went downhill. Consolidated says that Chase couldn’t raise the $5 million; Chase says Consolidated decided to keep Fuller Brush Company because the company had started making money. The parties broke off negotiations in January, and later Chase brought this suit.

The main issue at trial was whether the November 17 agreement was a contract to sell Fuller Brush Company to Chase. The jury found it was not, and Chase has not appealed this finding. But he argues that the jury may have found as it did only because the judge did not instruct it correctly concerning Newman’s apparent authority to bind Consolidated by his telegram of November 26, in which he said that the board of directors had approved the sale to Chase, though it had not. This was an important issue because Newman did not have actual authority to sell the Fuller Brush Company without getting the board’s approval. The November 17 agreement became a binding contract of sale (on November 26) only if Newman’s representation that the board had approved the sale was within the scope of his apparent authority to deal on Consolidated’s behalf.

After making clear that only the board of directors had actual authority to sell Fuller Brush Company and that Chase had “the burden of proving the agent’s authority to enter into the particular contract on which [Chase] rests his claim,” the judge did give an instruction on apparent authority; only it is not a model of clarity. It states: “Apparent authority of an agent for its principal must be based on word and acts of his principal, and cannot be based on anything that the agent himself has said or done. The acts of an agent may be later ratified by a principal.” The first sentence, which is the focus of Chase’s objections, was taken verbatim from an instruction submitted by Consolidated; the second was added by the district judge.

Apart from the confusing change from neuter to masculine gender, and the singular “word” rather than “words,” the problem with this instruction is that it is meant for a case where the principal is a human being rather than a corporation. Since a corporation can act only through agents, what does it mean to say that the agent’s apparent authority must be based on the words and acts of the principal rather than the agent? Maybe it means that, for the corporation to be bound, the appearance of authority must be created by agents other than the agent whose authority is in question. He cannot just bootstrap himself into a position where he can bind his principal. He must be invested with *569 apparent authority by the acts or statements or misleading omissions of other, and responsible, agents of his corporate principal. This interpretation would make the instruction a correct statement of Illinois agency law, see, e.g., Schoenberger v. Chicago Transit Authority, 84 Ill.App.3d 1132, 1137-38, 39 Ill.Dec. 941, 946, 405 N.E.2d 1076, 1081 (1980); but to assume that the jury so interpreted it would be unrealistic. Juries do not find it easy to understand the issues in commercial cases in the best of circumstances.

But we do not think the judge committed reversible error in giving this defective instruction and failing to give the instruction offered by Chase. That instruction was off the mark too. It states: “The actions of [various Consolidated officers including Newman] bind Consolidated if they acted within the powers Consolidated gave them or if Chase could reasonably have believed, based upon their titles, positions, actions, and the actions or inactions of Consolidated, that they were acting with Consolidated’s authority.” The problem is with the words, “or if Chase could reasonably have believed.” The instruction nowhere requires that Chase have actually believed that Newman or the others were acting with Consolidated’s authority. An appearance of authority that fools no one does not bind the principal. See, e.g., Minniti v. Cascade Employers Ass’n, Inc., 280 Or. 319, 329, 570 P.2d 1171, 1177 (1977); Restatement (Second) of Agency § 8, comment a, at p. 31 (1957).

The facts make this omission more than a technicality, for they strongly suggest that Chase knew perfectly well that Newman had no authority to bind the corporation to the sale of the Fuller Brush Company. Chase is a wealthy and experienced investor (he estimates his net worth to be $33 million). He must at least have suspected that the sale of an entire corporate division worth millions would (as it did) require the approval of the seller’s board of directors (see American Law Institute, Principles of Corporate Governance: Analysis and Recommendations, Tent.Draft No. 2, § 3.02, comment f, at pp. 70-71 (April 13, 1984)), and that Consolidated’s board would not approve the sale till the terms were fully worked out, which had not been done as of November 26. Nor would Consolidated be bound, under Illinois law, just by virtue of having given Newman some apparent authority to deal on its behalf by designating him as its secretary and general counsel. Even if it had given him the title of “president,” this would not have invested him with apparent authority to “make a contract on its behalf which is unusual and extraordinary,” that is, beyond the usual authority of a president, as a contract to sell a major corporate division would be. Sacks v. Helene Curtis Industries, Inc., 340 Ill.App. 76, 86, 91 N.E.2d 127, 132 (1950); see also id. at 88-89, 91 N.E.2d at 133; Restatement (Second) of Agency, supra, § 27, comment a, at p. 104.

As for the telegram of November 26, in which Newman stated that the board of directors had ratified the sale, not only had Calabro requested Newman to send the telegram but Calabro had dictated the critical statement in it — that the board had approved the agreement to sell Fuller Brush to Chase. The purpose of the telegram was to help Chase raise money for the deal by convincing lenders that the deal would go through. Then Chase would be able to pledge assets of Fuller Brush Company to whomever he borrowed money from to pay Consolidated — would, in other words, be able to arrange a leveraged buyout of the Fuller Brush Company and therefore not have to put up his own money after all. Given Calabro’s role in the preparation of the telegram, we find it hard to see how Chase can argue that Newman misled him as to what Consolidated’s board had done. But in any event the instruction offered by Chase would not have put before the jury the question whether Chase was actually misled.

The circumstances in which the telegram was sent also scotch Chase’s alternative theory of apparent authority, which is that Consolidated, by holding out Newman to the world as Consolidated’s corporate *570 secretary, clothed him with apparent authority to represent truthfully what the board had done at its meeting of November 26. This is a perfectly valid theory but it has no application to the facts, since the representation was supplied by Calabro, Chase’s agent, rather than Newman. In any event, if this theory was to be put to the jury, Chase was obliged to embody it in a clearer instruction than the one the judge quite properly refused to give.

With the circumstances so strongly suggestive of knowledge by Chase or Calabro that the board of directors had not approved the sale, that Newman had no authority to approve it on his own, and that he was not attempting to approve it in accommodating Calabro's request for help with Chase’s efforts to finance the deal, Chase had (and failed) to come up with a better instruction on apparent authority: an instruction that would tell the jury that, to find for Chase, it had to find not only that he could reasonably have believed that Newman was authorized to (and attempted to) sell the Fuller .Brush Company to Chase but also that he had actually believed these things.

The question of a trial judge’s obligation to instruct correctly when the party objecting to an erroneous instruction offers an erroneous substitute is a vexing one. On the one hand, it would be an unwelcome burden on our overworked district judges to obligate them to repair all defects in tendered instructions. Moreover, we would not want to give a party an incentive to submit an erroneous instruction that was excessively favorable to his client, hoping that the district court would give it but knowing that if this ploy failed and he lost the case he could get a new trial by renewing on appeal his objection to the instruction that had actually been given. On the other hand, it seems to take the premises of an adversary system just a little too seriously to let the judge read to the jury an instruction containing an error that was brought to his attention in timely fashion (so that the bar of Fed.R.Civ.P. 51 does not fall), merely because the substitute instruction offered by the objecting party was not itself completely free from error.

The way out of this dilemma is through a comparison of the gravity of the two errors — the error made by the party proposing the substitute instruction, and the error in the instruction that the judge gave. If the first is merely technical and the second substantial, the party’s error will be excused; but if the errors are of equal gravity, and a fortiori if the party’s error is substantial and the judge’s merely technical, the party will not be heard to complain about the error in the instruction that was given. The cases in this and other circuits support this approach. They ask how serious the error in the instruction given was, and whether the defect in the offered substitute was merely technical, en route to deciding whether the defect should be forgiven. See, e.g., Brandes v. Burbank, 613 F.2d 658, 668 (7th Cir.1980); Honeycutt v. Aetna Ins. Co., 510 F.2d 340, 349, n. 11 (7th Cir.1975); Celanese Corp. of America v. Vandalia Warehouse Corp., 424 F.2d 1176, 1181 (7th Cir.1970); Jones v. Miles, 656 F.2d 103, 107 n. 6 (5th Cir.1981); 9 Wright & Miller, Federal Practice and Procedure § 2552 at pp. 630-31 (1971).

Applying this standard here, we find no reversible error. The judge did not give a plainly wrong instruction; he gave an unclear, an incomplete, at worst a misleading instruction. And the substitute offered by the plaintiff was not marred by a merely technical error; it missed an essential point bearing on the issue of apparent authority — the plaintiff’s own knowledge that the board of directors had not approved the sale.

In any event we doubt that the exact wording of the instruction on apparent authority could have affected the jury’s verdict. As we said earlier, juries are not conversant with the fine points of agency and commercial law or easily educated in them. The issue in this case as the jury must have perceived it was whether Consolidated had tried to get out of the deal with Chase because Fuller Brush Company unexpectedly turned profitable, or whether *571 Chase had abandoned the deal because he couldn’t raise the cash. If the jury had thought the first it would have brought in a verdict for Chase. It must, then, have thought the second; and in fact the weight of the evidence inclined in that direction. Apparent authority was central to neither issue.

To put this point more technically, if the jury had thought that Consolidated had stopped negotiating with Chase after November 17 merely because Consolidated had decided it wanted to keep Fuller Brush Company after all, the jury could readily have concluded that Consolidated had violated a binding commitment in the November 17 agreement: a commitment to negotiate in good faith for the sale of Fuller Brush to Chase. As to that promise, the agreement — though merely a letter of intent — was (if the parties intended) an enforceable contract. See, e.g., Borg-Warner Corp. v. Anchor Coupling Co., 16 Ill.2d 234, 156 N.E.2d 513 (1958); Itek Corp. v. Chicago Aerial Industries, Inc., 248 A.2d 625, 629 (Del.1968); Reprosystem, B.V. v. SCM Corp., 522 F.Supp. 1257, 1273 (S.D.N.Y.1981), aff’d and rev’d, 727 F.2d 257, 264 (2d Cir.1984); Evans, Inc. v. Tiffany & Co., 416 F.Supp. 224, 239 (N.D.Ill.1976). Thus the jury may have found no binding contract because it thought that Chase, not Consolidated, had broken off the negotiations; there was, as we have said, much evidence to support such a conclusion.

But this observation points up Chase’s second ground of appeal, which is that the district court erroneously excluded evidence concerning negotiations with potential lenders. This evidence, which Chase says would have bolstered his contention that he could finance the deal — and had not abandoned it, as Consolidated contended— consisted mainly of (1) a memo, written by Calabro, which says, “National Acceptance — Likes the deal ... Waiting for contract and further details,” and (2) Calabro’s offer to testify that Kanes, the president of National Acceptance, told him the same thing orally.

The evidence would have been hearsay if offered to show that National Acceptance really did like the deal that Chase had worked out with Consolidated Foods. But it was not hearsay when offered to prove just that Chase had not backed out of the deal because he realized he couldn’t get financing: to show what he heard and understood, as opposed to the truth of what was said to him. See Fed.R.Evid. 801(c); 4 Weinstein & Berger, Weinstein’s Evidence ¶ 801(c)[01] at pp. 801-70 to 801-71 (1981). And this was the purpose, or at least a purpose, for which it was offered.

But the judge did not exclude the evidence (to the extent offered for this purpose) as hearsay. He excluded it because he thought the jury would misunderstand it, and treat it as evidence that Kanes intended to finance Chase’s purchase of the Fuller Brush Company. The judge may exclude otherwise admissible evidence “if its probative’ value is substantially outweighed by the danger of ... misleading the jury____” Fed.R.Evid. 403. Since the trial judge has the feel of the jury in a way that the appellate court cannot, his ruling will rarely be disturbed on appeal — and will not be in this case. The excluded evidence had only slight probative value (when taken with Kanes’ deposition), yet was potentially misleading. Kanes last met with Chase’s people 10 days before Calabro wrote the brief memo all but a few words of which we have quoted. Kanes testified in his deposition that he had made no commitment to lend funds to Chase, and it is more than likely that the memo and Calabro’s testimony concerned a brief, inconclusive, exploratory session of little relevance to the issue of why the deal between Chase and Consolidated fell apart.

Affirmed.