SWYGERT, Senior Circuit Judge.

Defendant Wayne T. Schmuck appeals from his conviction of twelve counts of mail fraud, 18 U.S.C. § 1341 (1982). Because the defendant was improperly denied an instruction on a lesser included offense, we reverse and remand for a new trial.

The defendant concedes that he willfully rolled back odometers in order to sell used cars for inflated prices, a federal misdemeanor. 15 U.S.C. § 1984, 1990c(a) (1982). Nevertheless, he was indicted of mail fraud only, a felony, and the district court denied his request that the jury be instructed on the odometer tampering offense as a lesser included offense of mail fraud.

The mail fraud statute requires a scheme to defraud and some mailing in furtherance of that scheme. According to the indictment and evidence at trial, the underlying scheme to defraud was the defendant's admitted odometer tampering. As for the mailing requirement, it is undisputed that the defendant did not personally use the mails to further his scheme. Rather, the unwitting retailers to whom the defendant sold the cars mailed forms, pursuant to the prevailing practice in Wisconsin, to the Secretary of State that included, inter alia, the defendant's fraudulent odometer readings. These forms were necessary to obtain a certificate of title. Without such a certificate, the cars were not marketable to the ultimate consumers.

I

The defendant urges outright reversal of his convictions on two grounds that can be dismissed summarily. First, he argues that no rational trier of fact could find that he used the mails in furtherance of his odometer-tampering fraud. In United States v. Galloway, 664 F.2d 161 (7th Cir. 1981), we held that a rational trier of fact could convict on a mail fraud charge arising from a virtually identical odometer tampering scheme that also entailed the same mailings of forms by third-party retailers. We refuse to overrule that decision.

Second, defendant contends that due process prohibits a mail fraud conviction based on a routine mailing by a third party that the defendant has no power to prevent. One answer is that he can prevent the mailing by abstaining from the fraud. In any event, this court in Galloway, 664 F.2d at 161, perceived no due process impediment to holding the same type of mailing a predicate for a mail fraud conviction. Nor did the Supreme Court when it said that a person causes the mails to be used if he "does an act with knowledge that the use of the mails will follow in the ordinary course of business, or where such use can reasonably be foreseen" even though use of the mails was not actually intended. Pereira v. United States, 347 U.S. 1, 8-9, 74 S.Ct. 358, 362-363, 98 L.Ed. 435 (1954).

Defendant argues that his convictions violated due process in still another respect because the mail fraud statute does not give fair warning that a fraud which causes a mailing in the manner present here is a violation of the statute. Regardless of what the defendant or any reasonable person might conclude upon reading the mail fraud statute in isolation, the expansive judicial interpretations of the language, going back many years, must be considered with the text, and leave no doubt that a fraud that foreseeably causes a mailing under the present circumstances is an offense.

II

The defendant also urges several grounds for a reversal and remand for a new trial. We need only reach the lesser included offense issue.

Defendant moved in advance of trial for an instruction that would have permitted the jury to find him guilty of odometer tampering. He was entitled to such an instruction if, under these facts, odometer tampering can properly be considered a lesser included offense of mail fraud and if a rational juror could have found him innocent of mail fraud but guilty of odometer tampering. See Fed.R.Crim.P. 31(c); Keeble v. United States, 412 U.S. 205, 208, 93 S.Ct. 1993, 1995, 36 L.Ed.2d 844 (1973).

We find that under these facts odometer tampering is a lesser included offense of mail fraud. It is possible, of course, to commit mail fraud without altering odometers. Apart from the mailing element, the mail fraud statute requires only some "scheme" to defraud. 18 U.S.C. § 1341. The scheme need not concern odometers, and even if it does, it need not be completed. The offense of odometers tampering, on the other hand, is necessarily concerned with odometers, and the tampering must be completed to be punishable under 15 U.S.C. § 1984, 1990c(a). This theoretical possibility of committing the greater offense without committing the lesser offense would be dispositive under the traditional definition of a lesser included offense; the lesser offense would lack the requisite identity of statutory elements with the greater offense. Two circuits continue to follow this traditional definition. See United States v. Campbell, 652 F.2d 760, 762 (8th Cir. 1981); Government of Virgin Islands v. Parrilla, 550 F.2d 879, 881 (3d Cir. 1977).

This circuit, however, does not follow the traditional definition. Rather than focus on theoretical possibilities, we look to the facts as alleged in the indictment and as proven at trial to determine whether the prosecution relied on proof of all the elements of the lesser offense to prove, in turn, guilt of the greater offense. See United States v. Cova, 755 F.2d 595, 597 (7th Cir. 1985); accord United States v. Zang, 703 F.2d 1186, 1196 (10th Cir. 1983); United States v. Johnson, 637 F.2d 1224, 1238-39 (9th Cir. 1980); United States v. Whitaker, 447 F.2d 314, 319 (D.C. Cir. 1971). Thus, it is beside the point that a scheme to defraud could have been sufficiently established without proof of all the statutory elements of odometer tampering. What matters is that according to the prosecution's theory of the case, as expressed in the indictment and at trial, the defendant did intentionally cause odometers to be rolled back, thereby satisfying all the elements of the odometer tampering statute.

To be sure, this more flexible definition of a lesser included offense carries with it the potential for abuse. The defendant might confuse the jury by securing instructions on a myriad of crimes only tangentially related to the one charged; as a result, the jury may feel pressured to return a compromise verdict even though it would otherwise be inclined to convict the defendant of the greater offense charged. We therefore join the District of Columbia Circuit in requiring the defendant, when requesting a lesser included instruction, to show some "inherent relationship" between the lesser offense proved and the greater offense charged. See Whitaker, 447 F.2d at 319.

An "inherent relationship" exists where the two offense relate to the protection of the same interests and where proof of the greater offense can generally be expected to require proof of the lesser offense. Id. If such is the case, there is little chance that the jury will be confused by the lesser included instruction. Rather, the instruction will alert the jury to its duty to decide not simply whether the defendant is guilty, but what he is guilty of. Where there is such an inherent relationship, the two offenses can properly be viewed as simply two different degrees of the same general crime, and the instruction informs the jury that different degrees of culpability can be ascribed to the defendant's wrongful conduct.

We hold that there is an inherent relationship between mail fraud and the "fraud" that underlies the mail fraud offense. Both offenses protect against the same kind of societal wrong: fraud. And it can generally be expected that proof of mail fraud will entail proof of a completed underlying "fraud," although this is certainly not always true. See supra at 1370-1371; cf. Whitaker, 447 F.2d at 319 (generally, though not invariably, proofs must overlap). Moreover, it is difficult to see how an instruction on the underlying fraud will confuse the jury. Congress has deemed fraud that is perpetrated through the mails to be an especially serious offense, punishable as a felony by as much as five years in jail for each mailing. But a misdemeanor fraud, such as odometer tampering, is deemed less threatening to society and carries a lesser penalty. An instruction on odometer tampering simply informs the jury that the defendant's conduct is less serious if it does not entail a sufficient abuse of the mails to come within the mail fraud statute and encourages the jury to make an informed judgment as to the degree of culpability.

Having found odometer tampering to be a lesser included offense of mail fraud, we turn to the second requirement that must be satisfied in order to be entitled to an instruction on the lesser offense: that a rational trier of fact could have found the defendant innocent of the greater offense, but guilty of the lesser offense. See Keeble, 412 U.S. at 208, 93 S.Ct. at 1995; United States v. Medina, 755 F.2d 1269, 1273 (7th Cir. 1985). The reason for this requirement is to ensure that the instruction is not "merely a device for defendant to invoke the mercy-dispensing prerogative of the jury." United States v. Sinclair, 444 F.2d 888, 890 (D.C. Cir. 1971); accord Medina, 755 F.2d at 1273; United States v. Busic, 592 F.2d 13, 24-25 (2nd Cir. 1978). And in a larger sense, this requirement prevents the judge and jury from encroaching on the other's domain. The jury resolves factual issues only; the judge decides the law. To be sure, the jury's decision to convict on the lesser rather than the greater offense should and does indirectly affect the defendant's ultimate punishment, an issue of law. But the jury makes such a decision only because it finds a factual element of the greater offense lacking; it cannot invade the province of the judge by deciding as a matter of law that, regardless of the facts, conviction of the lesser offense and the attendant lesser punishment are more appropriate. On the other hand, in deciding what a rational juror can and cannot conclude from the evidence, the court should be wary of invading the exclusive factfinding prerogatives of the jury.

As the literal terms of the test indicate, the courts will rarely deem a potential jury finding "irrational." This is in keeping with the policies that underlie the test: the object is merely to discourage the jury from rendering mercy verdicts without invading the jury's province as the ultimate finder of fact. In general, the courts will find irrationality only where the theory of the defense is logically inconsistent with a guilty verdict on the lesser offense or where evidence of such guilt is so slight as not to raise a jury question on the issue. In the first instance, the danger of encouraging jury misconduct is obvious. An illogical verdict is by definition irrational and is probably motivated by factors extrinsic to the evidence at trial — i.e., a desire to render a mercy verdict. Thus, if a defendant in a murder prosecution relies on an alibi defense, he can hardly ask the jury, in the alternative, to convict him of a lesser degree of homicide. Either he is guilty of murder or completely innocent; any other verdict would be an illogical compromise verdict. In such a case, the defendant is not entitled to a lesser included instruction. E.g., Briley v. Bass, 742 F.2d 155, 164-65 (4th Cir. 1984).

In the second instance, the courts will refuse to give the lesser instruction not because a verdict of guilty would be illogical or wholly unsupported by the evidence, but because the evidence to sustain the verdict is simply too thin to persuade a rational juror. See, e.g., Medina, 755 F.2d at 1273 n. 2; Busic, 592 F.2d at 24-25; Sinclair, 444 F.2d at 890. Yet if a rational juror should be expected to return verdicts that are plausible as well as merely logical or merely supported by some scintilla of evidence in the record, courts must take care to allow jurors to choose from a broad range of plausible verdicts. Thus, the courts draw all inferences in favor of finding the potential verdict rational. See Sinclair, 444 F.2d at 890. Where the verdict would require a bizarre or overly imaginative reconstruction of events, the verdict is irrational. See id. The classic example is where a defendant is found in possession of more than a ton of marijuana and is charged with possession with intent to distribute. Although it is possible that the defendant had no intent to distribute, such a possibility is so improbable that an instruction on the lesser offense of simple possession is improper. E.g., United States v. Silla, 555 F.2d 703, 706-07 (9th Cir. 1977).

Turning to the case at bar, an acquittal of mail fraud would have been logically consistent with a conviction of odometer tampering. Such a verdict would follow from a finding that the mailings were not sufficiently in furtherance of the underlying fraud to justify a mail fraud conviction.

As for the requirement that the verdict be rational and plausible as well as logical, such a conclusion of the mailings issue would have been substantially supported by the record evidence. This is not a case where the defendant presented little or no evidence on point. Cf. Busic, 592 F.2d at 25 (it is not enough that the defendant formally contested the existence of the additional element distinguishing the greater offense from the lesser; "[t]he contest must be real"). Indeed, the defendant rested his entire defense on the theory that the mailings element was lacking. The jury could have rationally and plausibly concluded that mailings by third-party retailers who were not under the control of the defendant did not sufficiently further the fraud to justify a conviction. True, the mailing of fraudulent odometer readings allowed the unwitting retailers to gain the certificate of title necessary to market the cars, which in turn encouraged them to continue to do business with the defendant. Yet the jury could have plausibly concluded that, on balance, the mailings were counterproductive to the fraud because they brought the fraudulent odometer readings to the attention of the authorities.

Alternatively, the jury could simply conclude that, aside from the counterproductive effect of the mailings, the mailings were too tangential to the success of the scheme to be deemed "in furtherance" of the scheme. Although the mailings here may have "furthered" the scheme in the literal sense of the word, it is clear that the statute requires something more. For in the modern economy, it is difficult to imagine a transaction that does not at some point involve some tangential use of the mails by some party at least remotely related to the defendant. Lest all fraud be subsumed by the mail fraud statute, the courts require that the mailings further the fraud in the sense that it is at least incidental to an essential element of the fraud. United States v. Lea, 618 F.2d 426, 430 (7th Cir.), cert. denied, 449 U.S. 823, 101 S.Ct. 82, 66 L.Ed.2d 25 (1980).

Whether the retailers' ability to secure title was essential to the defendant's scheme and whether the mailings of odometer readings to obtain such title were incidental to that end are questions for the jury. These are issues that involve difficult line-drawing problems; this is not a case where a conviction on the lesser offense would require bizarre or overly-imaginative inferences from the evidence. See Silla, 555 F.2d at 706-07; Sinclair, 444 F.2d at 890.

It is true that in Galloway, 664 F.2d at 161, we stressed that a jury could rationally convict on virtually identical facts. But we did not hold the opposite verdict to be irrational; we simply pointed out that the mailings issue was one for the jury to decide. Consistent with Galloway, we now hold that the jury could have rationally reached either verdict. Mailings by third parties not under the control of the defendant that indirectly, if at all, further the underlying fraud may or may not be sufficiently "in furtherance" of the fraud to justify a mail fraud conviction; the issue is one of fact, and the two opposite conclusions are both sufficiently plausible to be within the purview of the jury's rational discretion.

III

Because the defendant was entitled to an instruction on odometer tampering, we reverse his convictions and remand for a new trial. Circuit Rule 18 shall not apply.