OPINION
{1} Defendant, Armando Munoz, appeals his conviction on two counts of great bodily injury by vehicle (GBI). Defendant argues that the district court improperly refused his request for an instruction on the lesser offense of driving while intoxicated (DWI). Because we agree that Defendant was entitled to an instruction on the offense of driving-while intoxicated, we reverse his convictions and remand for a new trial.
BACKGROUND
{2} In the early morning hours of September 30, 2001, a SUV driven by Defendant collided with a motorcycle at the intersection of Sudderth Drive and Raines Drive in Ruidoso. The driver of the motorcycle and his passenger were severely injured. The only witnesses to the collision were the driver and passenger of the motorcycle; Defendant’s brother, who was a passenger in Defendant’s SUV; and Defendant.
*236{3} Defendant was charged, inter alia, with two counts of causing great bodily injury by vehicle, contrary to NMSA 1978, § 66-8-101 (B) and (C) (1991). At trial, the State’s theory was that Defendant caused the accident by pulling out of Raines Drive into the path of the motorcycle as it proceeded eastward on Sudderth Drive with the right of way. Defendant’s theory was that he was driving westward in the right-hand lane of Sudderth Drive and that the motorcycle veered over the centerline into his lane, causing the collision.
{4} The driver of the motorcycle conceded that he had been drinking prior to the collision. He testified that he had looked ahead prior to the accident and that Sudderth Drive was clear of traffic. The next thing he remembered was waking up in the hospital. The passenger testified that she recalled seeing an SUV matching the description of Defendant’s vehicle off to the right as the motorcycle approached Raines Drive. The passenger did not recall the collision itself.
{5} Defendant admitted that he had up to eight beers prior to the accident. The two samples analyzed in Defendant’s breath test showed values of 0.17 and 0.18 BAC.1 Defendant denied having been on Raines Drive that evening. Defendant told an investigating officer at the scene that he had been heading west on Sudderth Drive when the motorcycle struck his vehicle. Defendant’s brother testified that they were headed west on Sudderth Drive when the accident occurred.
{6} The State’s evidence included testimony by the investigating officers and an accident reconstructionist. Their testimony generally supported the State’s theory that the accident occurred in the eastbound side of Sudderth Drive, rather than the westbound side as claimed by Defendant.
{7} During a jury instruction conference, Defendant requested a jury instruction on DWI as a lesser-included offense of GBI by vehicle. Defendant argued that the State’s theory of the case was that Defendant’s impaired driving due to intoxication was the proximate cause of the collision. Defendant argued that under the State’s theory of the case, Defendant could not have committed GBI by vehicle without also having committed the offense of DWI. Defendant pointed out that without a DWI instruction, the only alternatives the jury would have would be letting Defendant go “Scott-free” or convicting him of GBI by vehicle. The State opposed the instruction, arguing that DWI was not a lesser-included offense of GBI by vehicle under the holdings of State v. Trujillo, 85 N.M. 208, 510 P.2d 1079 (Ct.App.1973) and State v. Tanton, 88 N.M. 333, 540 P.2d 813 (1975). Relying on Trujillo, the trial court denied Defendant’s requested instruction on DWI.
{8} The jury returned guilty verdicts on both counts of GBI by vehicle.
DISCUSSION
{9} Rule 5-611(D) NMRA 2004 of the New Mexico Rules of Criminal Procedure provides that “[i]f so instructed, the jury may find the defendant guilty of an offense necessarily included in the offense charged.” For purposes of Rule 5-611(D), we use the “terms ‘lesser-included’ and ‘necessarily-included’ interchangeably.” State v. Meadors, 121 N.M. 38, 41, n. 2, 908 P.2d 731, 734 n. 2 (1995). “The rules regarding lesser-included offenses developed at common law to aid the prosecution in cases in which its proof may have failed as to the higher offense charged but nonetheless was sufficient to support a conviction on a lesser offense.” 5 Wayne R. LaFave, et ah, Criminal Procedure § 24.8(d), at 574 (2d 1999). New Mexico common law extended the right to lesser-included offense instructions to defendants under appropriate circumstances. State v. Mitchell, 43 N.M. 138, 148-42, 87 P.2d 432, 433-34 (1939) (holding that trial court’s refusal of the defendant’s request for an instruction on simple assault in a prosecution for assault with a deadly weapon was reversible error where the evidence would have supported a verdict on simple assault). This *237entitlement is carried forward under Rule 5-611(D). Meadors, 121 N.M. at 47, 908 P.2d at 740 (observing that defendant’s right to a lesser-included offense instruction is “at least as great as the State’s right”).
{10} We review the propriety of a district court’s refusal to instruct on a lesser-included offense under a de novo standard. State v. Gaitan, 2002-NMSC-007, ¶ 10, 131 N.M. 758, 42 P.3d 1207.2
{11} In Meadors, the Supreme Court endorsed two alternative tests for determining whether a party is entitled to an instruction on a lesser-included offense. The first test endorsed by Meadors is the “strict elements” test, which requires a trial court to grant a request for an instruction on a lesser-included offense “when the statutory elements of the lesser crime are a subset of the statutory elements of the charged crime.” 121 N.M. at 44, 908 P.2d at 736. In addition, Meadors recognizes an entitlement to an instruction on a lesser offense where:
(1) the defendant could not have committed the greater offense in the manner described in the charging document without also committing the lesser offense, and therefore notice of the greater offense necessarily incorporates notice of the lesser offense; (2) the evidence adduced at trial is sufficient to sustain a conviction on the lesser offense; and (3) the elements that distinguish the lesser and greater offenses are sufficiently in dispute such that a jury rationally could acquit on the greater offense and convict on the lesser.
Id. The Supreme Court characterized this three-prong test as the “cognate approach.” Id.
{12} In Meadors, the party requesting the lesser-included offense instruction was the State. Id. at 41, 908 P.2d at 734. Subsequently, in State v. Darkis, 2000-NMCA-085, 129 N.M. 547, 10 P.3d 871, we addressed a defendant’s request for a lesser-included offense instruction. Applying the cognate approach endorsed by the Supreme Court in Meadors, we held that the trial court had improperly refused the defendant’s request for a lesser-included offense instruction. Darkis, 2000-NMCA-085, ¶ 19, 129 N.M. 547, 10 P.3d 871. We reversed the defendant’s conviction and remanded for a new trial. Id. ¶ 21. Darkis noted that the purpose of the first prong of the Meadors cognate approach is to protect the defendant’s right to notice of the charges against which he must defend. Id. ¶ 16. Because lack of notice to the defendant is not a concern when the defendant himself requests the instruction, Meadors, 121 N.M. at 42, 908 P.2d at 735, Darkis recognized that the notice-giving function of the charging document assumes a lesser role in evaluating a defendant’s request for a lesser-included offense instruction, and consequently that “a defendant’s right to a lesser-included offense instruction [under Meadors ] is effectively greater than the State’s.” Darkis, 2000-NMCA-085, ¶ 16, 129 N.M. 547,10 P.3d 871.
{13} In the present case, Defendant’s request for a lesser-included offense instruction on driving under the influence fails the strict elements test of Meadors. We understand the strict elements test to be similar to the test followed by federal courts in determining whether one offense is a “necessarily-included” offense under Rule 31(c) of the Federal Rules of Criminal Procedure. Meadors, 121 N.M. at 41-42, 908 P.2d at 734-35 (discussing federal practice under Schmuck v. United States, 489 U.S. 705, 109 S.Ct. 1443, 103 L.Ed.2d 734 (1989)). Under the strict elements test, if it is possible, considering the statutory elements of the charged offense in the abstract, to hypothesize a manner of committing the greater offense without also committing the lesser offense, then the lesser offense is not necessarily included in the greater. Schmuck, 489 U.S. at 721, 109 S.Ct. 1443 (comparing statu*238tory elements of mail fraud and odometer tampering; holding that the offense of odometer tampering is not a necessarily-included offense of mail fraud); State v. Patterson, 90 N.M. 735, 737, 568 P.2d 261, 263 (Ct.App.1977) (holding that for purposes of former Criminal Procedure Rule 44(d) aggravated assault with a deadly weapon is not a lesser-included offense of assault with intent to kill because assault with intent to kill can be committed without the use of a deadly weapon). Under the strict elements test, driving while under the influence of intoxicating liquor is not a lesser-included offense of homicide by vehicle because it is possible to commit homicide by vehicle without being intoxicated, as for example, by driving recklessly. Trujillo, 85 N.M. at 213-14, 510 P.2d at 1084-85.
{14} However, our conclusion that Defendant’s request failed the strict elements test does not end our inquiry. Turning to Meadors’s cognate approach, we conclude that Defendant’s request satisfies each of the three parts of the cognate approach.
{15} The first prong of the Meadors’s test is satisfied as each of the two counts in the complaint charging GBI by vehicle expressly refers to driving under the influence of intoxicating liquor as one of the alternative circumstances rendering Defendant’s operation of his vehicle unlawful.
{16} The second prong of the cognate approach also is satisfied. The evidence at trial included Defendant’s admission that he had been drinking, testimony by an investigating officer that Defendant smelled of alcohol and failed two field sobriety tests, and testimony relating the results of Defendant’s breath test showing results of 0.17 and 0.18%. This evidence was sufficient to support a conviction for DWI.
{17} The third prong of the cognate test is met by substantial evidence putting in dispute the element of causation. Generally, a jury has “the privilege to believe or to disbelieve any testimony it hears.” State v. Alberico, 116 N.M. 156, 164, 861 P.2d 192, 200 (1993). A jury that disbelieved the State’s witnesses and believed the testimony of Defendant and his brother could rationally find that even though Defendant was intoxicated, the accident was caused by the driver of the motorcycle, who veered across the centerline into the side of Defendant’s vehicle. Thus, causation, the element that distinguishes driving under the influence from GBI by vehicle under the facts of this case, was sufficiently in dispute that a jury rationally could have acquitted Defendant of GBI by vehicle and found Defendant guilty of driving under the influence.3
{18} The State argues that Trujillo and Tanton are controlling authority notwithstanding Meadors. We disagree. As we explain below, Trujillo and Tanton have been overtaken by the Supreme Court’s subsequent adoption of the cognate test.
{19} The defendant in Trujillo had been charged with homicide by vehicle while under the influence of intoxicating liquor or in the alternative while driving recklessly. Trujillo, 85 N.M. at 210, 510 P.2d at 1081. At trial, the defendant requested an instruction on the offense of driving under the influence of intoxicating liquor, contending that the evidence would have allowed the jury to find that the defendant had been driving while under the influence, but that his intoxication was not the proximate cause of the victim’s death. Id. at 213, 510 P.2d at 1084. The district court denied the requested instruction. Id. On appeal, we agreed that there was evidence establishing that the defendant had been driving under the influence. Id. Nonetheless, we affirmed the denial of the instruction, reasoning as follows:
Homicide by vehicle may be committed while driving under the influence of intoxicating liquor, but it may also be committed *239by driving while under the influence of drugs or reckless driving. Driving while under the influence of intoxicating liquor may be, but is not necessarily, an element of the homicide charge. The crime of homicide by vehicle may be committed without there being any driving while under the influence of intoxicating liquor. The converse is also true. The crime being distinct, driving while under the influence of intoxicating liquor is not an offense included within the homicide charge.
Id. at 213-14, 510 P.2d at 1084-85.
{20} Our analysis in Trujillo was akin to the “sub-set of the statutory elements” prong of Meadors. Meadors, 121 N.M. at 42, 908 P.2d at 735. Under a strict elements test, the denial of a lesser-included offense instruction under the facts of Trujillo was proper because it was possible, as we ourselves recognized, to hypothesize ways of committing homicide by vehicle that did not involve driving under the influence of intoxicating liquor — e.g., by driving recklessly, but sober; or by driving under the influence of drugs. Trujillo, 85 N.M. at 213, 510 P.2d at 1084. Under the cognate approach we are not confined to a comparison of the abstract statutory elements of the offenses. See Meadors, 121 N.M. at 44, 908 P.2d at 737 (applying the cognate approach by looking to both the greater offense, as described in the charging document, and the evidence adduced at trial). Moreover, as we understand Meadors, the cognate approach may be applied separately to each alternative means of committing the greater offense. Thus, Defendant’s right to an instruction on a lesser-included offense is not automatically defeated under the cognate approach merely because the State has charged alternatively.4 Because we obviously did not apply in Trujillo a test that was not adopted by the Supreme Court until years later in Meadors, Trujillo is not controlling authority where the party requesting a lesser-included offense instruction fails the strict elements test, but nevertheless is able to satisfy Meadors’s cognate approach. „
{21} For different reasons, we conclude that Tanton is not controlling. In Tanton, the defendant was charged in district court with homicide by vehicle while driving under the influence of intoxicating liquor, or, in the alternative, while driving recklessly. Tanton, 88 N.M. at 334, 540 P.2d at 814. The defendant argued that the prosecution in district court following an earlier conviction in municipal court on a charge of driving while under the influence of intoxicating liquor arising out of the same incident amounted to successive prosecutions in violation of the Double Jeopardy Clause. Id. Citing Trujillo, the Supreme Court rejected the defendant’s argument that driving under the influence of liquor was a lesser-included offense of homicide by vehicle:
A conviction or acquittal of a lesser offense necessarily included in a greater offense bars a subsequent prosecution for the greater offense. Ex parte Williams, 58 N.M. 37, 265 P.2d 359 (1954); State v. Medina, 87 N.M. 394, 534 P.2d 486 (Ct. App.1975)____[TJhis principle is not applicable in this case because the indictment charges in the alternative. The lesser offense of driving while under the influence of intoxicating liquor is not necessarily included in the greater offense of homicide by vehicle. State v. Trujillo, 85 N.M. 208, 510 P.2d 1079 (Ct.App.1973).
Id. at 335, 540 P.2d at 815 (emphasis added).
{22} The Supreme Court’s reliance on Trujillo in a double jeopardy context suggests that in 1975, when the Supreme Court decided Tanton, the Supreme Court viewed the test for determining whether two crimes were the “same offense” for double jeopardy purposes and the test for determining entitlement to a lesser-included offense instruction as largely interchangeable. Subsequently, the Supreme Court has recognized that although Bule 5-611(D) lesser-included of*240fense instruction jurisprudence and double jeopardy jurisprudence both employ the descriptive term “lesser-included offense,” they address different legal problems and bear only a “tangential relation” to each other. Swafford v. State, 112 N.M. 3, 12, 810 P.2d 1223, 1232 (1991).
{23} Tanton was decided prior to Meadors and in the context of a pretrial motion to dismiss on double jeopardy grounds. Tanton has little or no precedential value in determining Defendant’s entitlement under the Meadors cognate approach to a lesser-included offense instruction.
CONCLUSION
{24} The district court erred by denying Defendant’s request for an instruction on the lesser-included offense of DWI. We reverse Defendant’s convictions for GBI by vehicle under Counts I and II, vacate the Judgment and Sentence imposed as to Counts I and II, and remand for a new trial on Counts I and II.
{25} IT IS SO ORDERED.
JAMES J. WECHSLER, C.J. and RODERICK T. KENNEDY, J., concur.