In United States v. Schmuck, 776 F.2d 1368 (7th Cir.1985), a divided panel decided that under the facts of this mail fraud prosecution, the offense of knowing and *385willful odometer alteration was a lesser included offense within the charged offense of mail fraud. Defendant’s conviction was reversed, therefore, because it was error to refuse an instruction under Rule 31(c), F.R.Crim.P., on the possibility of finding defendant guilty of the odometer offense. Although odometer alteration is not a statutory element of mail fraud, the panel, relying on United States v. Whitaker, 447 F.2d 314 (D.C.Cir.1971), held that there is an inherent relationship between mail fraud and the “fraud” that underlies the mail fraud offense. 776 F.2d at 1371. Accordingly the odometer offense proved by the evidence constituted a lesser included offense for the purpose of Rule 31(c).
The panel decision was vacated and rehearing en banc granted. United States v. Schmuck, 784 F.2d 846 (7th Cir.1986). We now reject the Whitaker doctrine and decide that the odometer offense, though proved, was not a lesser included offense, or, as Rule 31(c) says “an offense necessarily included in the offense charged.” All other significant claims raised were correctly decided adversely to defendant in Part I of Judge Swygert’s opinion, 776 F.2d at 1369-70. We now adopt Part I and affirm.
I
Defendant Schmuck was convicted, after a jury trial, of 12 counts of mail fraud. Each count of the indictment alleged a scheme by Schmuck to defraud purchasers of used automobiles by representing that the automobiles had substantially less mileage than was true. Schmuck would purchase automobiles, cause their odometer readings to be altered, offer them to dealers, and provide purchasing dealers with an odometer statement reflecting the false mileage. The dealers would sell the cars to retail customers. Both the dealers and the customers would rely on the false readings and pay more than if readings had not been reduced. In order to obtain titles in the names of their customers, the dealers would mail Wisconsin title applications to the Wisconsin Department of Transportation. Each count of the indictment alleged the mailing of an application for title for an automobile by a dealer on a specified date. Five different dealers were named; three dealers made only one mailing, one made four, and one five. It was charged that Schmuck caused each mailing for the purpose of executing the scheme.
Pursuant to Rule 31(c), defendant moved prior to trial for an instruction that would have permitted the jury to convict him of odometer alteration as a lesser included offense of mail fraud, presumably on each count. That motion was denied. He was convicted and appealed.
In reversing and remanding for a new trial, the panel rejected the “traditional” definition of a lesser included offense, in favor of the “inherent relationship” approach first expounded in United States v. Whitaker, 447 F.2d 314 (D.C.Cir.1971). The traditional (elements) test requires identity of the elements of the two offenses, such that some of the elements of the crime charged themselves comprise a separate, lesser offense; to be necessarily included, the elements of the lesser offense must be a subset of the elements of the charged offense. See Sansone v. United States, 380 U.S. 343, 349-50, 85 S.Ct. 1004, 1009, 13 L.Ed.2d 882 (1965); Berra v. United States, 351 U.S. 131, 134, 76 S.Ct. 685, 688, 100 L.Ed. 1013 (1956); United States v. Campbell, 652 F.2d 760, 762 (8th Cir.1981); Government of the Virgin Islands v. Parrilla, 550 F.2d 879, 881 (3rd Cir.1977). Thus where the lesser offense requires an element not required for the greater offense, an instruction should be refused.1
*386Broadly speaking, there are two elements of an offense under the mail fraud statute: (1) having devised or intending to devise a scheme to defraud (or to perform specified fraudulent acts); and (2) use of mail for the purpose of executing the scheme or attempting to do so.2 It is not required that any part of the contemplated scheme be performed, although in practice fraudulent conduct usually is proved in order to establish the scheme. The odometer offense consists of knowingly and willfully altering or causing alteration of an odometer with intent to change the number of miles indicated.3 Each statute requires proof of facts not required by the other. The two offenses are separate. Blockburger v. United States, 284 U.S. 299, 304, 52 S.Ct. 180, 182, 76 L.Ed. 306 (1932).
In determining, for this purpose, the elements of the offense charged, the ordinary focus is upon the statute defining the offense. Where the statute prescribes an element in general language, capable of wide variation in types of conduct, e.g., mail fraud, falsification (18 U.S.C. § 1001), continuing criminal enterprise (21 U.S.C. § 848), RICO (18 U.S.C. § 1963), failure to perform any of several types of statutory duty (e.g., 26 U.S.C. § 7203) there is logical appeal for the proposition that the terms of the indictment will narrow the scope of the elements to be examined. See United States v. Stavros, 597 F.2d 108, 110 (7th Cir.1979); but see United States v. Kimberlin, 781 F.2d 1247, 1257 n. 10 (7th Cir.1985). Given the present indictment, however, alleging as one element devising a scheme to defraud purchasers of automobiles with altered odometers, knowingly and willfully causing an odometer to be altered is not identical to the element of having devised the scheme.
The District of Columbia Circuit rejected strict comparison of elements in favor of inquiry whether there was an “inherent relationship” between the crime charged and a lesser offense proved at trial. The defendant in Whitaker had been charged with first degree burglary, and his request for an instruction permitting conviction of the lesser offense of unlawful entry was denied, because the District of Columbia Code did not exclusively require unlawful entry as an element of first degree burglary, and therefore unlawful entry would not be a lesser included offense under the traditional test. However, because the proof showed that defendant had, in fact, committed the burglary by means of an unlawful entry, in reversing and remanding for a new trial, the court held that
[a] more natural, realistic and sound interpretation of the scope of “lesser included offense,” in line with our own views on the subject, is that defendant is entitled to invoke Rule 31(c) when a lesser offense is established by the evidence adduced at trial in proof of the greater offense, with the caveat that there must also be an “inherent” relationship between the greater and lesser offenses, i.e., they must relate to the protection of the same interests, and must be so related that in the general nature of these crimes though not necessarily invariably, *387proof of the lesser offense is necessarily presented as part of the showing of the commission of the greater offense.
447 F.2d at 319.
The Whitaker court went on to note that the Constitution and the common law require that the charge in the indictment give the defendant notice that he could also be convicted of any lesser included offenses, if the evidence s"o warrants. The prosecution as well as the defendant may seek an instruction pursuant to Rule 31(c) under the traditional test, because all elements of the lesser included offense have, by definition, been charged. Whitaker dispensed with the mutuality requirement, because of “considerations of justice and good judicial administration.... [T]he defense ought not to be restricted by the stringent constitutional limits upon the prosecutor’s right ... [and] doubt as to whether the prosecution could rightfully have requested such a charge should not bar the charge being given at the request of the defense.” Id. at 321.
Applying the Whitaker approach, the panel in the present case concluded that
there is an inherent relationship between mail fraud and the “fraud” that underlies the mail fraud offense.... [I]t can generally be expected that proof of mail fraud will entail proof of a completed underlying “fraud,” although this is certainly not always true.... 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.
776 F.2d at 1371.
Having found the requisite relationship between odometer alteration and mail fraud, the panel turned to the second requirement of the right to a lesser included offense instruction: whether the proof of the element necessary for the greater crime but not for the lesser crime is sufficiently in dispute so that a rational jury could find the defendant not guilty of the greater but guilty of the lesser. Keeble v. United States, 412 U.S. 205, 208, 93 S.Ct. 1993, 1995, 36 L.Ed.2d 844 (1973); Sansone v. United States, 380 U.S. 343, 350, 85 S.Ct. 1004, 1009, 13 L.Ed.2d 882 (1965); Berra v. United States, 351 U.S. 131, 134, 76 S.Ct. 685, 688, 100 L.Ed.2d 1013 (1956); United States v. Medina, 755 F.2d 1269, 1273 (7th Cir.1985). Whatever the test used to determine whether one offense is included within another, there is agreement that there must be a separable issue in the case as to the distinguishing element. Cf., e.g., United States v. Pino, 606 F.2d 908, 917 (10th Cir.1979) (inherent relationship approach) with United States v. Campbell, 652 F.2d 760, 763 (8th Cir.1981) (traditional test). The panel held that the jury could have rationally found that the mailings were counterproductive to the fraud because they brought the fraudulent readings to the authorities’ attention, or that the mailings were too tangential to the success of the scheme to be deemed “in furtherance” of the scheme.
II
A. Rule 31(c).
We reject the inherent relationship test,4 and hold that an offense is necessarily included within another for the purpose of Rule 31(c) only when the elements of the lesser offense form a subset of the elements of the charged offense.5 The ele*388ments approach is grounded in the terms and history of Rule 31(c), comports with the constitutional requirement of notice to defendant of the potential for conviction of an offense not separately charged, permits a greater degree of certainty in the application of Rule 31(c), and harmonizes the concept of “necessarily included” under Rule 31(c) with that of a lesser included offense where the issue is double jeopardy.
Although the Supreme Court has not spoken directly to this issue,6 we believe that decisions involving Rule 31(c) motions suggest the Court’s adherence to the traditional method. In Keeble v. United States, 412 U.S. 205, 93 S.Ct. 1993, 36 L.Ed.2d 844 (1973), the Court held the defendant entitled to an instruction on a lesser included offense. The Court compared the statutory elements of the offense charged — assault with intent to commit serious bodily injury — with those of the offense on which an instruction was sought — simple assault — stating
an intent to commit serious bodily injury is a necessary element of the crime with which petitioner was charged, but not of the crime of simple assault. Since the nature of petitioner’s intent was very much in dispute at trial, the jury could rationally have convicted him of simple assault if that option had been presented.
Id. at 213, 93 S.Ct. at 1998. The Court did note the Whitaker decision and that it had dispensed with mutuality as a necessary prerequisite to the defendant’s right to a lesser included offense instruction. The Court found it unnecessary to decide that question. Id. at 214 n. 14, 93 S.Ct. at 1998 n. 14.
Similarly, in Sansone v. United States, 380 U.S. 343, 85 S.Ct. 1004, 13 L.Ed.2d 882 (1965), the elements of violation of § 7201 of the Internal Revenue Code of 1954, willful tax evasion, were compared with those of § 7207, willful filing of a fraudulent or false return, and § 7203, willful failure to pay taxes when required, to determine whether the latter misdemeanors were offenses included within the felony charged under § 7201. The Court determined that petitioner was not entitled to a lesser included offense instruction because on the facts of the case, the three statutes covered the same ground. The Court said that “§ 7201 necessarily includes among its elements actions which, if isolated from the others, constitute lesser offenses” and instruction should be given if a jury could rationally find that “although all the ele*389ments of § 7201 have not been proved, all the elements of one or more lesser offenses have been” proved. Id. at 351, 85 S.Ct. at 1010; see also Berra v. United States, 351 U.S. 131, 134, 76 S.Ct. 685, 688, 100 L.Ed. 1013 (1956) (“where some of the elements of the crime charged themselves constitute a lesser crime, the defendant, if the evidence justified it, would no doubt be entitled to an instruction”).
These cases counsel in favor of the elements test because the Court examined and compared statutory elements in deciding whether the lesser offense was necessarily included in the offense charged. The decisions nowhere suggest any different inquiry into the relationship between offenses, nor any relaxation of the traditional test where a lesser offense proved could be deemed inherently related to the charged offense.
The statutory elements test is also faithful to the text of Rule 31(c), where the critical phrase is “necessarily included in the offense charged.” The inherent relationship approach in effect reads out “necessarily included in” and substitutes something like “factually related to and serves the same policy goals as” the charged offense. Neither the court in Whitaker nor any decision adopting its analysis has addressed how the language of the Rule gives rise to the inherent relationship test.
The text of the Rule makes no distinction between a motion made by the defendant or by the government. Yet the inherent relationship approach requires that motions by the government and the defendant be treated differently, because the charge of the greater offense does not give notice that defendant is facing a charge of a lesser offense all the elements of which are not identical to elements of the charged offense. If the determination whether the crimes are sufficiently related is not made until all the evidence is developed at trial, the defendant may not have had notice constitutionally sufficient to support an instruction at the prosecution’s request. Thus, the relationship test dispenses with the requirement of mutuality without explaining how the text of the Rule supports a different result depending upon who makes the motion.
Moreover, the history of the Rule suggests that it codified the traditional approach. “At common law the jury was permitted to find the defendant guilty of any lesser offense necessarily included in the offense charged. This rule originally developed as an aid to the prosecution in cases in which the proof failed to establish some element of the crime charged.” Beck v. Alabama, 447 U.S. 625, 633, 100 S.Ct. 2382, 2387, 65 L.Ed.2d 392 (1980); United States v. Cova, 755 F.2d 595, 597 (7th Cir.1985); see 2M Hale, Pleas of the Crown 301-02 (1736); Rex v. Withal & Overend, 168 Eng.Rep. 146 (1772). In 1872, this concept was enacted as a statute,7 now contained in Rule 31(c). The advisory Committee Notes state that the Rule is a “restatement of existing law.” See Keeble, 412 U.S. at 208 n. 6, 93 S.Ct. at 1995 n. 6. Thus, there is no indication that the Rule was intended to abrogate the traditional approach to lesser included offenses, including the availability of an instruction in aid of the Government, nor can the Supreme Court’s recognition of the defendant’s right to an instruction be read as an endorsement of any nonmutual restrictions on the Government.
A significant consideration is the inherent relationship test’s lack of certainty and predictability. See United States v. Johnson, 637 F.2d 1224, 1238 (9th Cir.1980) (statutory approach “may be appealing in its promise of certainty and intellectual purity”). Finding an inherent relationship requires a determination that the offenses relate to the same interests and that “in general” proof of the lesser “necessarily” involves proof of the greater. Whitaker, 447 F.2d at 319. These new layers of analysis add to the uncertainty of the propriety of an instruction in a particular case: not only are there more issues to be resolved, but correct resolution involves *390questions of degree and judgment, with the attendant probability that the trial and appellate courts may differ.
Another problem with relaxation of the traditional test is that relaxation may well permit defendants to seek a lenient outcome by requesting a lesser included offense instruction on every lesser offense that could possibly be made out from the evidence. This tendency to misuse the Rule was recognized in Whitaker, and is the reason why the Whitaker court required that there must be an inherent relationship between the lesser offense and the offense charged. 447 F.2d at 319.
We find, on balance, no persuasive reason to substitute the Whitaker doctrine for the traditional approach.8
B. Double Jeopardy and Cumulative Punishment.
Rule 31(c) uses the language, “an offense necessarily included in the offense charged.” Many of the decisions on a Rule 31(c) problem use the term “lesser included offense.” The “lesser included offense” concept is also significant in determining certain claims of double jeopardy or unlawful cumulative punishment. See Brown v. Ohio, 432 U.S. 161, 97 S.Ct. 2221, 53 L.Ed.2d 187 (1977).
It seems desirable that, as nearly as possible, the terminology should have the same meaning in both contexts. Using the elements test for Rule 31(c) problems at least approaches keeping the same meaning.
It is at least arguable that in the double jeopardy and cumulative punishment contexts the requisite identity of elements is to be determined solely from comparison of the two statutes, and that the indictment does not narrow the type of elements to be examined. Brown, 432 U.S. at 168, 97 S.Ct. at 226; Blockburger v. United States, 284 U.S. 299, 304, 52 S.Ct. 180, 182, 76 L.Ed. 306 (1932); United States v. Woodward, 469 U.S. 105, 108, 105 S.Ct. 611, 612, 83 L.Ed.2d 518; United States v. Kimberlin, 781 F.2d 1247, 1255-57 (7th Cir.1985), cert. denied, — U.S. -, 107 S.Ct. 419, 93 L.Ed.2d 370 (1986). The focus is “on the proof necessary to prove the statutory elements of each offense, rather than on the actual evidence to be presented at trial.” Illinois v. Vitale, 447 U.S. 410, 416, 100 S.Ct. 2260, 2265, 65 L.Ed.2d 228 (1980). We need not decide in the case before us whether the allegations of the indictment will properly narrow the scope of the statutory elements to be examined in a given case.
The judgment appealed from is Affirmed.
. Several courts have listed five conditions to be met where a Rule 31(c) instruction is requested. The second is "the elements of the lesser offense must be identical to part of the elements of the greater offense" and the fifth "in general the chargeability of lesser included offenses rests on a principle of mutuality, that if proper, a charge may be demanded by either the prosecution or defense.” Whitaker, 447 F.2d at 317; United States v. Campbell, 652 F.2d 760, 761 (8th Cir.1981); United States v. Chapman, 615 F.2d 1294, 1299 (10th Cir.), cert. denied, 446 U.S. 967, 100 S.Ct. 2947, 64 L.Ed.2d 827 (1980); but see n. 5 infra, as to Tenth Circuit position. Another *386formulation is that the lesser offense must be such that it is impossible to commit the greater offense without having committed the lesser. Government of Virgin Islands v. Aquino, 378 F.2d 540, 554 (3rd Cir.1967). "The lesser included offense doctrine does not apply where the lesser offense includes an element, such as possession, not required for the greater offense." Campbell, 652 F.2d at 763.
. 18 U.S.C. § 1341 provides:
Whoever, having devised or intending to devise any scheme or artifice to defraud, or for obtaining money or property by means of false or fraudulent pretenses, representations, or promises, or to sell, dispose of, loan, exchange, alter, give away, distribute, supply, or furnish or procure for unlawful use any counterfeit or spurious coin, obligation, security, or other article, or anything represented to be or intimated or held out to be such counterfeit or spurious article, for the purpose of executing such scheme or artifice or attempting so to do, places in any post office or authorized depository for mail matter, any matter or thing whatever to be sent or delivered by the Postal Service, or takes or receives therefrom, any such matter or thing, or knowingly causes to be delivered by mail according to the direction thereon, or at the place at which it is directed to be delivered by the person to whom it is addressed, any such matter or thing, shall be fined not more than $1,000 or imprisoned not more than five years, or both.
. 15 U.S.C. § 1984 provides:
No person shall disconnect, reset, or alter or cause to be disconnected, reset, or altered, *387the odometer of any motor vehicle with intent to change the number of miles indicated thereon.
§ 1990c(a) prescribes a misdemeanor penalty for knowing and willful violation of any provision of the subchapter, including § 1984.
. The author of this opinion also adheres to his previously expressed view that there is no inherent relationship between odometer alteration and mail fraud even if the Whitaker doctrine were to prevail. 776 F.2d at 1373-75, Fairchild, J., concurring in part, dissenting in part.
. The Second Circuit states the test in terms of elements. See United States v. Lo Russo, 695 F.2d 45, 52 n. 3 (2d Cir.1982), cert. denied sub nom. Errante v. United States, 460 U.S. 1070, 103 S.Ct. 1525, 75 L.Ed.2d 948 (1983). We have found no case, however, where the Second Circuit has rejected the Whitaker approach. The Third Circuit states the elements test and asserts *388specifically "[t]he elements of the offense are compared in the abstract, without looking to the facts of the particular case." Government of Virgin Islands v. Joseph, 765 F.2d 394, 396 (3rd Cir.1985). The Eighth Circuit has adhered to the elements test, noting, but taking no position on, the question of abandoning mutuality. United States v. Campbell, 652 F.2d 760, 762-63 (8th Cir.1981).
Decisions of the Fourth Circuit, see United States v. Carter, 540 F.2d 753, 754 (4th Cir.1976), and the Fifth Circuit, see United States v. Williams, 775 F.2d 1295, 1302 (5th Cir.1985), cert. denied, 475 U.S. 1089, 106 S.Ct. 1477, 89 L.Ed.2d 732 (1986), are consistent with the elements approach.
Circuits adopting the inherent relationship test are the District of Columbia, Whitaker, 447 F.2d 314 (D.C.Cir.1971); and the Ninth, United States v. Martin, 783 F.2d 1449, 1451-53 (9th Cir.1986).
The Tenth Circuit adopted the Whitaker doctrine in a 1979 decision, United States v. Pino, 606 F.2d 908, 914-17 (10th Cir.1979). In a 1980 decision, the court stated the traditional test, including the requirement of mutuality. United States v. Chapman, 615 F.2d 1294, 1298-99 (10th Cir.), cert. denied, 446 U.S. 967, 100 S.Ct. 2947, 64 L.Ed.2d 827 (1980). In 1982, the court applied the Whitaker doctrine, citing Pino, but not Chapman. United States v. Zang, 703 F.2d 1186, 1196 (10th Cir.), cert. denied sub nom. Porter v. United States, 464 U.S. 828, 104 S.Ct. 103, 78 L.Ed.2d 107 (1983). Zang happened to be a prosecution for mail fraud. The scheme to defraud involved overcharging for crude oil by miscertification of the “tier” of the oil. Such miscertification was a violation of EPA regulations, and the court found this violation was not a lesser included offense because there was no inherent relationship between it and mail fraud. In 1987, the Tenth Circuit relied on Pino and Whitaker in affirming the conviction of a lesser offense, one element of which was not included in the offense charged. USA v. Cooper, 812 F.2d 1283 (10th Cir.1987). The dissenting judge would approve the Whitaker doctrine where a defendant requested the instruction, but concluded that in the case before the court, defendant had been convicted of an offense not charged.
. The Court has articulated a statutory elements test for a lesser included offense for double jeopardy purposes. See, infra, p. 390.
. ‘‘[I]n all criminal cases the defendant may be found guilty of any offence the commission of which is necessarily included in that with which he is charged in the indictment....” 17 Stat. 197, 198 (1872).
. In United States v. Cova, 755 F.2d 595 (7th Cir.1985), defendants were charged with conspiracy to distribute cocaine. The district court found insufficient evidence, but submitted an amended charge of conspiracy to possess, and defendants were convicted. Although there was no discussion of Whitaker, this court affirmed, holding that conspiracy to possess (proved) was a lesser included offense of the charged conspiracy to distribute. Id. at 599. Because it is possible fpr persons acquiring lawful possession to conspire to distribute, the elements test seems not to have been fulfilled. To the extent that Cova stands for a permitted departure from the elements test, it is overruled. See also reference to Cova in United States v. Kimberlin, 781 F.2d 1247, 1256-57, and n. 10.