
660 F.3d 880 (2011)
Noel AUSTIN, Petitioner-Appellant,
v.
Burl CAIN, Warden, Louisiana State Penitentiary, Respondent-Appellee.
No. 10-30342.
United States Court of Appeals, Fifth Circuit.
October 17, 2011.
*881 Noel Austin, Angola, LA, Pro Se.
Thomas Joseph Butler, Asst. Dist. Atty., Gretna, LA, for Respondent-Appellee.
Before KING, GARZA and GRAVES, Circuit Judges.
PER CURIAM:
On April 11, 2003, Petitioner-Appellant Noel Austin was arrested in a sting operation after attempting to sell cocaine to a confidential informant. When the authorities moved in to make the arrest, Austin unsuccessfully sought to flee the scene in his sports utility vehicle, and in the process nearly ran over several arresting officers. Austin was convicted of two counts of attempted first degree murder, one count of possession with intent to distribute cocaine, and one count of aggravated battery, and was sentenced to four concurrent terms of imprisonment. The court later imposed a life sentence on the first *882 count of attempted first degree murder due to Austin's status as a habitual offender. Austin's conviction was affirmed on direct appeal, and state habeas relief was denied. He subsequently filed a petition for writ of habeas corpus under the Antiterrorism and Effective Death Penalty Act, 28 U.S.C. § 2254, raising several grounds for relief, including a violation of the Double Jeopardy Clause of the Fifth Amendment. The district court denied relief. We granted a certificate of appealability as to Austin's double jeopardy claim only. We affirm the district court's judgment denying Austin's habeas corpus petition.

I. FACTUAL AND PROCEDURAL BACKGROUND
On the evening of April 11, 2003, law enforcement officers with the Louisiana State Police Gulf Coast High Intensity Drug-Trafficking task force ("HIDO"), in cooperation with the Drug Enforcement Administration ("DEA"), executed a sting operation outside a restaurant in Jefferson Parish, Louisiana. With the assistance of a confidential informant and undercover DEA Agent Carlton Simmons ("Simmons"), HIDO officers arranged for the purchase of one kilogram of cocaine from Petitioner-Appellant Noel Austin ("Austin") for $21,500. Several members of the Jefferson Parish Sheriff's Office assisted the state police in this operation.
On the night in question, Austin arrived in a sports utility vehicle and parked in the restaurant's parking lot. He walked between his vehicle and the restaurant several times, and eventually met an individual in another car (later identified as his brother) who handed him an unidentified item. Austin then met with both the confidential informant and Agent Simmons inside the restaurant to arrange the details of the purchase. After leaving the restaurant, Simmons returned to his car, while Austin and the confidential informant walked over to Austin's parked vehicle. The informant soon confirmed that Austin had the cocaine in his possession, and communicated this to Agent Simmons. Simmons relayed this information to the other officers, who then moved in to make the arrest.
Several law enforcement officers surrounded Austin's parked vehicle, and ordered him to surrender. Instead, Austin backed out of the parking space and towards two officers, who quickly moved out of the way. Austin then collided with an undercover vehicle, but kept driving. One officer fired at Austin's vehicle as it swerved and narrowly missed a fellow officer. Three other officers then stood in front of the vehicle and repeatedly ordered Austin to stop. Austin did not heed their warning, and instead accelerated towards them. The officers then fired at the vehicle, and Austin swerved at the last minute.
After nearly running over several officers, Austin drove out of the restaurant parking lot, ran over a median in the street, and crashed into a light pole in a nearby parking lot. A pursuing officer then fired into the vehicle after hearing what he thought sounded like gunshots (although it was later determined that Austin was not armed). Finding that Austin had been shot, the police called for the paramedics. Upon arrival, the paramedics cut open Austin's pant leg, at which point a kilogram of cocaine fell to the ground. The cocaine was later determined to have a street value of between $100,000 and $200,000.
On October 9, 2003, the Jefferson Parish District Attorney filed an eight count bill of information against Austin, charging him with six counts of attempted first degree murder in violation of LA.REV.STAT. § 14:27 and 14:30(A), corresponding to *883 the six law enforcement officers on the scene (counts one through six), one count of possession of more than 400 grams of cocaine in violation of LA.REV.STAT. § 40:967(F) (count seven), and one count of possession with intent to distribute cocaine in violation of LA.REV.STAT. § 40:967(A) (count eight). Importantly, the six counts of attempted first degree murder did not specify which of the applicable statutory circumstances under Section 14:30(A) (specific intent to kill a police officer, intent to kill more than one person, or intent to kill while engaged in cocaine distribution) provided the basis for the charges. The state later dismissed count seven, but went to trial on the remaining counts.
Austin was found guilty on counts one, two, and eight, and guilty of the responsive verdict of aggravated battery on count five. On March 4, 2004, the trial court sentenced Austin to concurrent prison terms of fifty years for each attempted murder conviction, ten years for the aggravated battery conviction, and thirty years for the possession with intent to distribute cocaine conviction. Pursuant to LA.REV. STAT. § 15:529.1, the state subsequently filed a "habitual offender bill of information" against Austin based upon his prior convictions for cocaine distribution in 1991 and for attempted murder in 1995. Following a hearing, the trial court found Austin to be a third time felony offender, vacated his original sentence as to count one, and imposed a sentence of life imprisonment without parole, probation, or suspension of sentence, to run concurrently with the sentences on the other counts.
Austin's sentences were affirmed on direct appeal, and his petition for state habeas relief was denied. See State v. Austin, 900 So.2d 867 (La.App. 5 Cir.2005) (direct appeal); 916 So.2d 143 (La.2005) (denial of writ of certiorari); 963 So.2d 389 (La.2007) (denial of writ of habeas corpus). Austin timely filed his petition for writ of habeas corpus in the district court on December 6, 2007. In his habeas petition, Austin argued that (1) he was denied protection against double jeopardy, (2) he was denied effective assistance of counsel, (3) he was denied a fair trial because the trial court failed to consider or declare a mistrial due to mid-trial prejudicial publicity, and (4) the trial court erred in denying his motion to reveal the identity of the confidential informant. The magistrate judge recommended that habeas relief be denied. Austin v. Cain, No. 07-9362, 2009 WL 6319555 (E.D.La. Oct. 16, 2009). The district court adopted this recommendation over Austin's objections, and denied a certificate of appealability ("COA"). Austin v. Cain, No. 07-9362, 2010 WL 1294060 (E.D.La. Mar. 26, 2010).
We granted a COA as to Austin's double jeopardy claim only, specifically to consider whether Austin was subjected to double jeopardy based upon his conviction and sentence for both possession with intent to distribute cocaine under LA.REV. STAT. § 40:967(A)(1) and attempted first degree murder under LA.REV.STAT. § 14:30, where the attempted first degree murder conviction could have been based on a specific intent to kill or inflict great bodily harm upon a person while engaged in the distribution of cocaine, as provided by LA. REV.STAT. § 14:30(A)(6).[1]


*884 II. STANDARD OF REVIEW
This habeas proceeding is subject to the Antiterrorism and Effective Death Penalty Act ("AEDPA"), 28 U.S.C. § 2254, as Austin filed his habeas petition on December 6, 2007, well after the effective date of AEDPA. Lindh v. Murphy, 521 U.S. 320, 324-26, 336, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997). Under AEDPA, a federal court may not grant a petitioner habeas relief on a claim that was adjudicated on the merits by the state court unless the state court decision was (1) "contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court," or (2) "was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding." 28 U.S.C. § 2254(d)(1), (2). The phrase "clearly established Federal law, as determined by the Supreme Court," "refers to the holdings, as opposed to the dicta, of [the Supreme] Court's decisions as of the time of the relevant state-court decision." Williams v. Taylor, 529 U.S. 362, 412, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000).
"An unreasonable application of federal law is different from an incorrect application of federal law. Indeed, a federal habeas court may not issue the writ simply because that court concludes in its independent judgment that the relevant state-court decision applied clearly established federal law erroneously or incorrectly. Rather, that application must be objectively unreasonable.... AEDPA thus imposes a highly deferential standard for evaluating state-court rulings, and demands that state-court decisions be given the benefit of the doubt." Renico v. Lett, ___ U.S. ___, 130 S.Ct. 1855, 1862, 176 L.Ed.2d 678 (2010) (citations and internal quotation marks omitted). The decision of a state court is "deemed contrary to clearly established federal law if it reaches a legal conclusion in direct conflict with a prior decision of the Supreme Court or if it reaches a different conclusion than the Supreme Court based on materially indistinguishable facts." Gray v. Epps, 616 F.3d 436, 439 (5th Cir.2010) (citing Williams, 529 U.S. at 404-08, 120 S.Ct. 1495). A state court's factual findings are "presumed to be correct," although a habeas petitioner may rebut this presumption by "clear and convincing evidence." 28 U.S.C. § 2254(e)(1).
In an appeal of the district court's denial of habeas relief, "this court reviews the district court's findings of fact for clear error and its conclusions of law de novo, applying the same standard of review that the district court applied to the state court decision." Jones v. Cain, 600 F.3d 527, 535 (5th Cir.2010).

III. DISCUSSION

A. Concurrent Sentence Doctrine
Before turning to the merits, we first address the argument of Respondent-Appellee Burl Cain ("the State") that this court should decline federal habeas review of Austin's claim under the concurrent sentence doctrine. The State argues that Austin's sentence as to count one (attempted first degree murder) was enhanced to life imprisonment without parole, and that even if Austin could prevail on the merits of his double jeopardy claim, the maximum habeas relief available would be the invalidation of his thirty-year sentence with respect to count eight (possession with intent *885 to distribute cocaine).[2] As such, he would still serve a life sentence without the benefit of parole, probation, or suspension of sentence on count one, and a fifty year sentence on count two.
We decline to apply the concurrent sentence doctrine in this case. See 13C CHARLES ALAN WRIGHT & ARTHUR R. MILLER, FEDERAL PRACTICE AND PROCEDURE § 3533.4.2 (3d ed. 2011) ("[T]he [concurrent sentence] doctrine is a matter of appellate discretion, designed to serve the convenience of the courts; it can be put aside without need for further explanation."). It is true that this court has applied the concurrent sentence doctrine in circumstances similar to the case presently before us. For example, in Williams v. Maggio, 714 F.2d 554, 555-56 (5th Cir. 1983), we affirmed the district court's application of the doctrine in a habeas action after concluding that no adverse collateral consequences would result from the unreviewed conviction. We explained:
even assuming that [Williams could prevail on the merits of his claim], the maximum habeas relief available would be the invalidation of one of the sentences, and as the two sentences here are strictly identical in length, it would not matter which one were set aside. Moreover, because Williams was sentenced in each case as a third-time offender, he is not eligible either for parole on or diminution of either sentence.
Id. at 556. This court has, when possible, applied the doctrine "in a manner that removes the adverse collateral consequences of the sentence from the defendant," and has "adopted the policy of vacating the unreviewed sentence and suspending imposition of that sentence." United States v. Stovall, 825 F.2d 817, 824 (5th Cir.1987); see also United States v. Harrelson, 754 F.2d 1182, 1185 (5th Cir.1985); United States v. Cardona, 650 F.2d 54, 58 (5th Cir.1981).
We have, however, only infrequently applied the concurrent sentence doctrine in the state habeas context over the past thirty years. See Scott v. Louisiana, 934 F.2d 631, 635 (5th Cir.1991); Williams, 714 F.2d at 556. In fact, we are unaware of any decisions in which this court has applied the doctrine to a state habeas petition after enactment of AEDPA in 1996. Cf. 13C CHARLES ALAN WRIGHT & ARTHUR R. MILLER, FEDERAL PRACTICE AND PROCEDURE § 3533.4.2 (3d ed. 2011) ("Not many of the cases invoking the doctrine post-date 1987.... But the doctrine still is invoked on occasion."). The State cites one recent decision, Davis v. Thaler, 373 Fed.Appx. 446 (5th Cir.2010), in support of its concurrent sentence doctrine argument. In that case, however, the district court applied the concurrent sentence doctrine to vacate a sentence for a lesser included offense. The panel granted a COA to determine whether the district court's application of the doctrine was erroneous. After the state conceded the existence of a clear double jeopardy violation, however, the panel declined to consider whether the doctrine was applicable because the petitioner had already "received the maximum habeas relief available when the district court vacated his aggravated assault conviction." Id. at 450-51. In so holding, the panel raised but declined to answer the question of whether "the [concurrent sentence] doctrine is applicable for a state court conviction after AEDPA." Id. at *886 450. We also decline to address this issue here.[3]

B. Double Jeopardy
Austin, proceeding pro se, offers few specific arguments in support of his double jeopardy claim. In essence, he contends that possession with intent to distribute cocaine and attempted first degree murder are the "same offense" for double jeopardy purposes because the attempted first degree murder statute "requires proof of La. R.S. 40:967(A) [cocaine distribution]." He further argues that the state relied upon his cocaine distribution as a basis for proving attempted first degree murder at trial, and he is being punished twice for the same offense, in violation of the Double Jeopardy Clause.
The Louisiana Fifth Circuit Court of Appeal rejected Austin's double jeopardy argument on direct appeal. The court first explained:
When proof of a felony is an essential element of an attempted first degree murder, double jeopardy precludes conviction and punishment of the defendant for both attempted murder and the underlying felony. However, an accused who commits separate and distinct offenses during the same criminal episode or transaction may be prosecuted and convicted for each offense without violating the principle of double jeopardy.
Austin, 900 So.2d at 884 (citations omitted). The court then found that the state "did not specify the subsection of La.R.S. 14:30 with which it intended to proceed in the bill of information, and the trial judge charged the jury on subsections La.R.S. 14:30(A)(2), (3), and (6)." Id. Although the jury was not polled as to the particular subsection used to convict Austin, the court reasoned that the "attempted murder convictions can be upheld if there is sufficient evidence based on any of the alternative theories with which the jury was charged." Id. The court held that there was sufficient evidence to prove that Austin "committed attempted first degree murder by specifically intending to kill police officers under La.R.S. 14:30(A)(2)." Id. at 884-85. The court concluded that, "[b]ecause the State proved the attempted first degree murder convictions under La. R.S. 14:30(A)(2) as specific intent crimes, proof of possession of cocaine with intent to distribute was not an essential element." Id. at 885. Therefore, the court found no double jeopardy violation. In reaching its conclusion, the court cited state authority interpreting the Double Jeopardy Clause, rather than federal authority. The district court found that the state court's analysis did "not represent an unreasonable application of Supreme Court law to the facts of the instant case." Austin, 2009 WL 6319555, at *6.
For the reasons discussed herein, we conclude that the state appellate court's rejection of Austin's double jeopardy argument was not unreasonable in its factual or legal conclusions, 28 U.S.C. § 2254(d)(1), (2), and the district court properly denied habeas relief.

1. Background
The Double Jeopardy Clause of the Fifth Amendment provides that no person shall "be subject for the same offence to be twice put in jeopardy of life or limb." U.S. CONST. amend. V. This constitutional *887 guarantee is applicable to the states through the Due Process Clause of the Fourteenth Amendment. Benton v. Maryland, 395 U.S. 784, 794, 89 S.Ct. 2056, 23 L.Ed.2d 707 (1969). The Double Jeopardy Clause "protects against a second prosecution for the same offense after acquittal. It protects against a second prosecution for the same offense after conviction. And it protects against multiple punishments for the same offense." Brown v. Ohio, 432 U.S. 161, 165, 97 S.Ct. 2221, 53 L.Ed.2d 187 (1977) (internal quotation marks omitted) (quoting North Carolina v. Pearce, 395 U.S. 711, 717, 89 S.Ct. 2072, 23 L.Ed.2d 656 (1969)).
The longstanding test for determining whether two statutes constitute the "same offense" for double jeopardy purposes was first developed in Blockburger v. United States, 284 U.S. 299, 52 S.Ct. 180, 76 L.Ed. 306 (1932). There, the Supreme Court explained that "where the same act or transaction constitutes a violation of two distinct statutory provisions, the test to be applied to determine whether there are two offenses or only one, is whether each provision requires proof of a fact which the other does not." Id. at 304, 52 S.Ct. 180. A court applying the Blockburger test must "focus[ ] on the statutory elements of the offense. If each requires proof of a fact that the other does not, the Blockburger test is satisfied, notwithstanding a substantial overlap in the proof offered to establish the crimes." Iannelli v. United States, 420 U.S. 770, 785 n. 17, 95 S.Ct. 1284, 43 L.Ed.2d 616 (1975); see also United States v. Agofsky, 458 F.3d 369, 371 (5th Cir.2006) ("Under the Blockburger test, each offense must contain an element not contained in the other; if not, they are the same offense ... and double jeopardy bars subsequent punishment or prosecution.") (internal quotation marks omitted).

2. Analysis of Double Jeopardy Claim
Our analysis of Austin's double jeopardy claim must begin with the relevant statutes in this case. The version of Louisiana Revised Statute Section 14:30 in effect at the time Austin committed his offenses provided for seven alternatives through which first degree murder could be established, three of which are relevant here. The statute provided in relevant part as follows:
(A) First degree murder is the killing of a human being:
. . .
(2) When the offender has a specific intent to kill or to inflict great bodily harm upon a fireman, peace officer, or civilian employee of the Louisiana State Police Crime Laboratory or any other forensic laboratory engaged in the performance of his lawful duties, or when the specific intent to kill or to inflict great bodily harm is directly related to the victim's status as a fireman, peace officer, or civilian employee.
(3) When the offender has a specific intent to kill or to inflict great bodily harm upon more than one person.
. . .
(6) When the offender has the specific intent to kill or to inflict great bodily harm while engaged in the distribution, exchange, sale, or purchase, or any attempt thereof, of a controlled dangerous substance listed in Schedules I, II, III, IV, or V of the Uniform Controlled Dangerous Substances Law.
LA.REV.STAT. § 14:30(A)(2), (3), (6) (2003). The offense of possession with intent to distribute cocaine provided: "it shall be unlawful for any person knowingly or intentionally: (1) To produce, manufacture, distribute, or dispense or possess with intent *888 to produce, manufacture, distribute, or dispense, a controlled dangerous substance or controlled substance analogue classified in Schedule II." LA.REV.STAT. § 40:967(A)(1). Cocaine was listed in Schedule II as a controlled substance at the time of the offense. LA.REV.STAT. § 40:964(II)(A)(4).
In this case, the state did not specify in the bill of information the subsection under which it brought the six counts of attempted first degree murder, and evidence existed to support all three grounds noted above. Although the prosecution primarily relied upon the first alternative at trial (intent to kill a police officer), it did at times argue the third ground (cocaine distribution) to the jury, and the trial court instructed the jury on all three grounds. As the state court recognized, the jury returned only a general verdict and was not polled as to which of the three grounds furnished the basis of the attempted first degree murder convictions. The State argues at length that Austin's attempted first degree murder charges were based solely on Section 14:30(A)(2) (intent to kill or inflict great bodily harm on police officers), and not at all upon Section 14:30(A)(6). While we agree with the State that the record tends to support this position,[4] we cannot entirely rule out the possibility that subsection six was an additional basis for the prosecution and verdict.[5] More importantly, our purpose here is not to make an independent assessment of the record, but instead to determine the reasonableness of the state court's decision. 28 U.S.C. § 2254(d). As noted above, the state court found that there was sufficient evidence to prove attempted first degree murder under Section 14:30(A)(2), and that the state did in fact prove that subsection. The court did not conclude that Austin's attempted first degree murder charges were based solely on Section 14:30(A)(2), but rather only that proof of possession of cocaine with intent to distribute "was not an essential element" of the murder convictions. 900 So.2d at 885. We do not believe these findings to be "an unreasonable determination of the facts in light of the evidence presented in the State court proceeding." 28 U.S.C. § 2254(d)(2). Based on these factual determinations, we now must address whether the state court's resolution of Austin's double jeopardy claim is objectively unreasonable in light of clearly established federal law, as *889 determined by the Supreme Court. 28 U.S.C. § 2254(d)(1); Renico, 130 S.Ct. at 1862.
The most relevant Supreme Court decision in the context of this case is Illinois v. Vitale, 447 U.S. 410, 100 S.Ct. 2260, 65 L.Ed.2d 228 (1980), abrogated on other grounds by United States v. Dixon, 509 U.S. 688, 704, 113 S.Ct. 2849, 125 L.Ed.2d 556 (1993).[6] There, the petitioner had accidentally struck and killed two children while driving his vehicle, and was cited at the scene for failure to reduce speed. One child died at the scene of the accident, and the other child died the next day. Approximately one month later, Vitale appeared in court, pled not guilty to the charge of failure to reduce speed, and was found guilty after a short bench trial. The day after his conviction, Vitale was charged with involuntary manslaughter, based upon the same incident. Id. at 412-13, 100 S.Ct. 2260. On appeal, the Supreme Court addressed whether the Double Jeopardy Clause prohibited Illinois from prosecuting Vitale for involuntary manslaughter, after he had previously been convicted of failing to reduce speed. Id. at 411, 100 S.Ct. 2260. The Court began its analysis by considering "whether the offense of failing to reduce speed to avoid an accident is the `same offense' for double jeopardy purposes as the manslaughter charges" at issue. Id. at 415-16, 100 S.Ct. 2260. The Court explained:
[I]f manslaughter by automobile does not always entail proof of a failure to slow, then the two offenses are not the "same" under the Blockburger test. The mere possibility that the State will seek to rely on all of the ingredients necessarily included in the traffic offense to establish an element of its manslaughter case would not be sufficient to bar the latter prosecution.
Id. at 419, 100 S.Ct. 2260 (emphasis added). The Court then instructed, "[i]f, as a matter of Illinois law, a careless failure to slow is always a necessary element of manslaughter by automobile, then the two offenses are the `same' under Blockburger and Vitale's trial on the latter charge *890 would constitute double jeopardy under Brown v. Ohio [432 U.S. at 161, 97 S.Ct. 2221]." Id. at 419-20, 100 S.Ct. 2260 (emphasis added).[7] The Court then remanded the case to allow the state court to determine the relationship between the offenses of failure to slow and vehicular manslaughter under Illinois law.
In its opinion, the Vitale Court discussed its earlier holding in Brown that a conviction for a lesser-included offense precludes later prosecution for a greater offense. The Court explained that a double jeopardy violation existed in Brown because the defendant had been convicted of joyriding (taking a vehicle without the owner's consent) as well as auto theft, and "[t]he Ohio courts had held that every element of the joyriding is also an element of the crime of auto theft." Id. at 417, 100 S.Ct. 2260 (internal quotation marks omitted). It was therefore not possible to prove auto theft without also proving joyriding. The Vitale Court noted, however, that if the prosecution in Brown had been "able to prove auto theft, without also proving that the defendant took, operated, or kept the auto without the consent of the ownerif proof of the auto theft had not necessarily involved proof of joyriding the successive prosecutions would not have been for the `same offense' within the meaning of the Double Jeopardy Clause." Id. (emphasis added).
Even prior to Vitale, the Supreme Court had focused upon the essential or necessary elements of separate offenses to determine if they were in fact the "same" for double jeopardy purposes. In Harris v. Oklahoma, 433 U.S. 682, 97 S.Ct. 2912, 53 L.Ed.2d 1054 (1977), the petitioner was first convicted of felony murder after shooting a store clerk during a robbery, and later convicted on the separate charge of robbery with firearms based upon the same incident. The petitioner objected on double jeopardy grounds, as robbery was the only lesser-included offense that could have served as the predicate for the felony murder charge. The Supreme Court reversed the conviction for the lesser offense, and explained, "[w]hen, as here, conviction of a greater crime, murder, cannot be had without conviction of the lesser crime, robbery with firearms, the Double Jeopardy Clause bars prosecution for the lesser crime, after conviction of the greater one." Id. at 682, 97 S.Ct. 2912 (emphasis added). Three years after Harris, the Supreme Court decided Whalen v. United States, 445 U.S. 684, 100 S.Ct. 1432, 63 *891 L.Ed.2d 715 (1980). In that case, the petitioner had been convicted in the Superior Court of the District of Columbia for rape and for killing the same victim in the perpetration of the rape. The petitioner received consecutive sentences for each conviction. On appeal, the Supreme Court applied Blockburger in concluding that rape and a killing committed in the course of a rape constitute the "same offense," since "[a] conviction for killing in the course of a rape cannot be had without proving all the elements of the offense of rape." Id. at 693-94, 100 S.Ct. 1432. The government had argued that felony murder and rape were not the "same" offense under Blockburger, because the former offense did not in all cases require proof of rape, but rather the statute "proscribe[d] the killing of another person in the course of committing rape or robbery or kidnaping or arson, etc." Id. at 694, 100 S.Ct. 1432. The Court rejected this argument, and explained:
Where the offense to be proved does not include proof of a rapefor example, where the offense is a killing in the perpetration of a robberythe offense is of course different from the offense of rape, and the Government is correct in believing that cumulative punishments for the felony murder and for a rape would be permitted under Blockburger. In the present case, however, proof of rape is a necessary element of proof of the felony murder, and we are unpersuaded that this case should be treated differently from other cases in which one criminal offense requires proof of every element of another offense.
Id. (emphasis added).
This court has applied Vitale on multiple occasions, primarily in the context of felony-murder prosecutions.[8] In Sekou v. Blackburn, 796 F.2d 108 (5th Cir.1986), the court addressed whether a conviction for armed robbery and a subsequent plea to felony murder violated the Double Jeopardy Clause, when the criminal activity underlying the felony murder charge included a kidnapping in addition to the armed robbery. Id. at 109. The court held that "the Double Jeopardy Clause does not bar successive prosecutions for felony-murder and an underlying felony (regardless of which prosecution is first), so long as the specific underlying felony which is the subject of the earlier (or later) prosecution does not form the sole basis for the felony-murder prosecution." Id. (emphasis added). In doing so, the court distinguished Harris and Brown, and relied upon Vitale. The court explained, "in the present appeal, if the state could have proved felony-murder without also proving armed robbery, then the successive prosecutions do not constitute prosecutions for the `same offense' within the meaning of the Double Jeopardy Clause." Id. at 111 (citing Vitale, 447 U.S. at 417, 100 S.Ct. 2260). The court cautioned, however, that "once the state tried and convicted Sekou for armed robbery, it was barred from prosecuting him for felony-murder only if the sole underlying felony upon which that prosecution was based was the armed robbery." Id. (emphasis added). The court then examined whether the state had "bound itself to proving only armed robbery" at the defendant's felony-murder trial. The court found "absolutely no indication that the state intended to prove only the armed robbery as the basis for a felony-murder conviction," as the "state just as easily could have proven the kidnapping as the underlying felony." Id. In a footnote, the court noted that "the government may have put on evidence of both the *892 kidnapping and the armed robbery since both those crimes were part of the course of criminal activity leading to the murder. We read nothing in Vitale which would have prevented the government from proving both the kidnapping and the armed robbery if Sekou had gone to trial on the felony-murder charge." Id. at 111 n. 3. The court thus rejected Sekou's double jeopardy argument. Id. at 111-12.
In contrast, we found a double jeopardy violation in Neville v. Butler, 867 F.2d 886 (5th Cir.1989). We first restated that the Double Jeopardy Clause does not require invalidation of "convictions of both felony murder and a felony arising out of the same occurrence where it is shown that another separate felony could have served as the predicate offense underlying the felony murder conviction." Id. at 889 (emphasis added) (citing Sekou, 796 F.2d at 111). We ultimately found a double jeopardy violation, however, because "petitioner was convicted of both armed robbery and attempted felony murder predicated on the same armed robbery offense." Id. at 890-91.
Taken together, Vitale, Sekou, and Neville demonstrate that two offenses are the "same" under Blockburger only if one offense is "always a necessary element" of another offense. Vitale, 447 U.S. at 419, 100 S.Ct. 2260; Sekou, 796 F.2d at 111; Neville, 867 F.2d at 889. In contrast, where an offense constitutes only one of several alternative elements of another offense, the two are not the "same offense" for double jeopardy purposes. As applied here, we conclude that no double jeopardy violation occurred in Austin's case. It is clear that the lesser offense (possession with intent to distribute cocaine) is not "always a necessary element" of the greater offense (first degree murder) under Louisiana law. Vitale, 447 U.S. at 419, 100 S.Ct. 2260. Put another way, first degree murder does not "always entail proof" of possession with intent to distribute cocaine. Id. Rather, at the time of Austin's offense, first degree murder could be proven in seven different ways, three of which are directly at issue here. Moreover, we need not speculate as to the specific grounds the state used to prove attempted first degree murder. The prosecution was based on three alternatives, namely that Austin had a specific intent to kill or to inflict great bodily harm (1) upon a police officer, (2) upon more than one person, or (3) while engaged in cocaine distribution. LA.REV.STAT. § 14:30(A)(2), (3), (6). The state appellate court on direct review reasonably concluded that the state sought to prove (and did in fact prove) specific intent murder of police officers under subsection (A)(2), as a constitutionally valid basis for the attempted first degree murder charge. Austin, 900 So.2d at 884-85; 28 U.S.C. § 2254(d)(2).[9] Cocaine distribution was therefore not a necessary element of Austin's attempted first degree murder charge.
The Louisiana Fifth Circuit Court of Appeal correctly recognized and applied the principles that we have detailed above, even though it did not directly cite federal authority. The court instead relied upon Louisiana precedent that interpreted the *893 Double Jeopardy Clause of the Fifth Amendment, the analogous provision of the Louisiana Constitution,[10] and relevant Supreme Court precedent. Austin, 900 So.2d at 884-85 (citing State v. Brown, 694 So.2d 435, 437 (5th Cir.2005); State v. Barton, 857 So.2d 1189, 1201 (La.App. 5 Cir.2003); State v. Jackson, 767 So.2d 848, 853 (La.App. 5 Cir.2000)). We have explained that "a federal habeas court is authorized by Section 2254(d) to review only a state court's `decision,' and not the written opinion explaining that decision." Neal v. Puckett, 286 F.3d 230, 246 (5th Cir.2002) (en banc). Further, "our focus on the `unreasonable application' test under Section 2254(d) should be on the ultimate legal conclusion that the state court reached," and "the only question for a federal habeas court is whether the state court's determination is objectively unreasonable." Id. (emphasis added); see also Santellan v. Cockrell, 271 F.3d 190, 193 (5th Cir.2001) ("[AEDPA] compels federal courts to review for reasonableness the state court's ultimate decision, not every jot of its reasoning."). The state court properly concluded that no double jeopardy violation occurred because there was sufficient evidence to support the attempted first degree murder convictions based upon Austin's intent to kill police officers, and "proof of possession of cocaine with intent to distribute was not an essential element." Austin, 900 So.2d at 885.
In sum, we hold that the Louisiana Fifth Circuit Court of Appeal's decision regarding Austin's double jeopardy claim was neither contrary to, nor involved an unreasonable application of, clearly established federal law, as determined by the Supreme Court. The decision also did not involve "an unreasonable determination of the facts in light of the evidence presented in the State court proceeding." 28 U.S.C. § 2254(d)(1), (2). The district court properly denied Austin's petition for a writ of habeas corpus.

IV. CONCLUSION
For the foregoing reasons, we AFFIRM the judgment of the district court.
NOTES
[1]  Although Austin was sentenced to concurrent rather than consecutive prison terms, concurrent sentences may still constitute "multiple punishments" for double jeopardy purposes. See Ball v. United States, 470 U.S. 856, 864-65, 105 S.Ct. 1668, 84 L.Ed.2d 740 (1985) ("The second conviction, whose concomitant sentence is served concurrently, does not evaporate simply because of the concurrence of the sentence. The separate conviction, apart from the concurrent sentence, has potential adverse collateral consequences that may not be ignored."); United States v. Britt, 112 Fed.Appx. 352, 357 (5th Cir.2004) ("The Supreme Court [in Ball] has clearly stated that even concurrent sentences can comprise multiple punishments violative of the Double Jeopardy Clause.").
[2]  See United States v. Buckley, 586 F.2d 498, 505 (5th Cir. 1978) ("[W]here a defendant is improperly convicted for a lesser included offense, the proper remedy is to vacate both the conviction [a]nd sentence on the included offense, leaving the conviction and sentence on the greater offense intact.").
[3]  The Seventh Circuit has recently applied the doctrine in the state habeas context. See Cheeks v. Gaetz, 571 F.3d 680, 689-90 (7th Cir.2009). The Ninth Circuit, in contrast, has abandoned the doctrine altogether. United States v. De Bright, 730 F.2d 1255, 1259 (9th Cir. 1984) (en banc) ("We overrule our prior cases which have authorized use of the concurrent sentence doctrine.").
[4]  For example, in his opening statement, the prosecutor said, "at the conclusion of this case, we're certain that the State of Louisiana will stand before you and ask you to find Noel Austin guilty of six counts of attempted murder of police officers, as well as guilty as charged of possession with the intent to distribute a kilogram of cocaine." A similar statement was made during closing argument, where the prosecutor explained: "[Austin is] charged with six counts of attempting to commit first degree murder by attempting to kill a number of law enforcement officers, and he's charged with one count of possessing with intent to distribute cocaine." In his conclusion, the prosecutor argued, "[h]e took steps to kill six people who were out there to protect and defend the people of our parish. That's why it's first degree murder, because it's an attempt to kill police officers .... Ladies and gentlemen, we have proved beyond a reasonable doubt that this Defendant... attempted to kill six police officers, and that he possessed with an intent to distribute cocaine."
[5]  Notably, the prosecutor's statement during closing argument listed all three possible bases for an attempted first degree murder conviction:

[I]n order to prove the Defendant guilty of attempted first degree murder, we have to prove that he intended to kill law enforcement officers, or he intended to kill more than one person, or that he was engaged in the distribution or attempted distribution of a controlled dangerous substance and intended to kill someone, and took a step in furtherance of that intent.
[6]  In United States v. Dixon, 509 U.S. 688, 113 S.Ct. 2849, 125 L.Ed.2d 556 (1993), the Supreme Court overruled its prior decision in Grady v. Corbin, 495 U.S. 508, 110 S.Ct. 2084, 109 L.Ed.2d 548 (1990), which had held that "the Double Jeopardy Clause bars a subsequent prosecution if, to establish an essential element of an offense charged in that prosecution, the government will prove conduct that constitutes an offense for which the defendant has already been prosecuted." 495 U.S. at 510, 110 S.Ct. 2084 (emphasis added). The Grady Court relied in part upon the earlier "suggestion" in Vitale that "even if two successive prosecutions were not barred by the Blockburger test, the second prosecution would be barred if the prosecution sought to establish an essential element of the second crime by proving the conduct for which the defendant was convicted in the first prosecution." Id. In Dixon, the Court found that the Grady "same-conduct" test lacked "constitutional roots," and was "wholly inconsistent with earlier Supreme Court precedent and with the clear common-law understanding of double jeopardy." 509 U.S. at 704, 113 S.Ct. 2849. Vitale's dicta therefore was adopted in Grady, but then expressly rejected in Dixon.

At the same time, however, the Supreme Court made clear in Dixon that "Vitaleunquestionably reads Harris [v. Oklahoma, 433 U.S. 682, 97 S.Ct. 2912, 53 L.Ed.2d 1054 (1977)] as merely an application of the double jeopardy bar to lesser and greater included offenses." Id. at 707, 113 S.Ct. 2849. The Court also rejected the contention that Vitale in fact adopted a "same conduct" test. Id. ("Justice Souter instead elevates the statement in Vitale that, on certain hypothetical facts, the petitioner would have a `substantial' `claim' of double jeopardy on a Grady-type theory ... into a holding that the petitioner would win on that theory .... No Justice, the Vitale dissenters included, has ever construed this passage as answering, rather than simply raising, the question on which we later granted certiorari in Grady.").
[7]  We recognize that Vitale involved successive prosecutions, while the case before us involves potential multiple punishments after one prosecution. Nevertheless, the Double Jeopardy Clause has the same meaning in both contexts. In Dixon, the Supreme Court rejected Justice Souter's attempt to distinguish between the "successive prosecution" and "successive punishment" application of the Clause. 509 U.S. at 704, 113 S.Ct. 2849. Rather, the Court explained, "[w]e have often noted that the Clause serves the function of preventing both successive punishment and successive prosecution, but there is no authority, except Grady, for the proposition that it has different meanings in the two contexts. That is perhaps because it is embarrassing to assert that the single term `same offence' (the words of the Fifth Amendment at issue here) has two different meaningsthat what is the same offense is yet not the same offense." Id. (citation omitted). The Supreme Court has also recognized that, "[i]f two offenses are the same under [Blockburger] for purposes of barring consecutive sentences at a single trial, they necessarily will be the same for purposes of barring successive prosecutions. Where the judge is forbidden to impose cumulative punishment for two crimes at the end of a single proceeding, the prosecutor is forbidden to strive for the same result in successive proceedings." Brown, 432 U.S. at 166, 97 S.Ct. 2221 (citations omitted). Therefore, the relevant question is whether in fact two offenses are the "same" under Blockburger, regardless of whether the question arises in a multiple prosecution or multiple punishment context.
[8]  Louisiana's felony murder statute is not at issue here. Louisiana's felony murder statute is codified at LA.REV.STAT. § 14:30(A)(1), and Austin was not charged under this provision.
[9]  The state court's determination is supported by the fact that the jury convicted Austin of only two of the six counts of attempted first degree murder (of Agents Danny Jewell and Michael Pizzolato). This strongly suggests that subsection (A)(2) (murder of police officers), and perhaps (A)(3) (intent to kill more than one person) provided the primary bases for the verdict. If the jury had in fact relied upon subsection (A)(6) (cocaine distribution), there would have been little reason for it to differentiate between the victims, as Austin's cocaine distribution was ongoing throughout the incident, and not specific to particular victims.
[10]  Article 1, Section 15 of the Louisiana Constitution of 1974 provides, "[n]o person shall be twice placed in jeopardy for the same offense, except on his application for a new trial, when a mistrial is declared, or when a motion in arrest of judgment is sustained." LA. CONST. art. 1, § 15.
