POLITZ, Circuit Judge:

Ivrin Bolden, Jr., currently a prisoner at West Tennessee High Security Facility, appeals the district court’s denial of his 28 U.S.C. § 2254 petition which relates to a Louisiana state conviction. For the reasons assigned, we affirm.

BACKGROUND

Bolden was tried in Louisiana state court in 1988 for the murder of Brenda Spicer. He testified at trial and denied killing or having had physical contact with her. The jury acquitted. Bolden later confessed to killing Spicer and was charged with perjury for his testimony at the murder trial.

Because a detailed factual background of this high-profile case is provided in the opinions of the Louisiana Supreme Court 1 and the Louisiana Third Circuit Court of Appeals, 2 we need only summarize the facts relevant to this appeal. On March 6, 1987 the body of Brenda Spicer, a former basketball player at Northeast Louisiana University, was found in a trash dumpster on campus in Monroe, Louisiana. The coroner stated that the victim had been killed by strangulation at approximately 7:00 p.m. the previous evening. The coroner found sperm in the victim’s rectum and vagina, and saliva on the victim’s breasts.

Bolden was tried for Spicer’s murder. The State sought to demonstrate that Bol- *581 den murdered Spicer because he was jealous of her close relationship with his girlfriend, Joel Tillis. The State’s case was largely circumstantial; no eyewitnesses testified that Bolden had physical contact with or murdered Spicer. The State’s theory of the case was that Bolden took Spi-cer to a storage locker unit on March 5, 1987, murdered her, and then went to a campus basketball game. At half-time Bolden allegedly went back to the storage locker and moved Spicer’s body to the dumpster. To bolster this theory, the State presented evidence that Spicer met Bolden at approximately 5:45 p.m., that Bolden attended the basketball game and was taking pictures on the floor to establish an alibi, and that Bolden was seen running away from the basketball arena at half-time. Physical tests performed on the seminal fluid and saliva indicated a type A secretor, a category in which Bolden and 80% of the population belong.

At trial, Bolden testified on his own behalf as follows:

Q. Did you meet Brenda Spicer at that storage locker on March 5th?

A. No, I did not at any time that day.

Q. The only time you saw Brenda Spi-cer is when she gave you that camera and the $5.00?

A. I saw her earlier in the dorm and the last time I saw her was at the intersection when she had given me the camera.

Q. Did you have any kind of physical struggle or contact with Brenda Spicer that day?

A. No, I didn’t, didn’t have any contact with her at all physically.

Q. Did you have any kind of sexual intercourse with Brenda Spicer?

A. Never did.

Q. You never have?

A. No, I haven’t.

Q. Did you kill Brenda Spicer on March 5th?

A. No, I did not.

The jury acquitted Bolden of Spicer’s murder.

Bolden and Tillis later moved to Tennessee. In 1989, Tillis disappeared and her body was found in Arkansas. Bolden, although a suspect in her murder, was never arrested and eventually moved to New Jersey and began to live with Jennifer Spurlock. In 1991, Bolden filed a complaint against Spurlock with local police in New Jersey. During the investigation of this complaint, Bolden admitted to killing Joel Tillis and Brenda Spicer. 3 Bolden pled guilty in Tennessee to involuntary manslaughter in the death of Tillis and received a ten-year sentence.

Bolden was charged in Louisiana with perjury in connection with his testimony in Spicer’s murder trial. Prior to the perjury trial, Bolden moved to dismiss the charges as violating the collateral estoppel component of the double jeopardy clause of the fifth amendment, a motion which the state trial court denied. The Louisiana Supreme Court affirmed the trial court’s ruling and remanded the case for further *582 proceedings. The court found that the perjury prosecution was not barred by the murder trial because the jury could have found that reasonable doubt was present in the first trial. Specifically, the court noted that this was not a situation in which the jury was presented with two conflicting versions of the facts and was forced to determine the veracity of one over the other, as would have been the case if there had been eyewitness testimony contradicting defendant’s statements. 4

Additionally, assuming arguendo that the jury necessarily determined Bolden’s credibility in the murder trial, the Louisiana Supreme Court enunciated a rule of law, relying primarily on the dicta of other courts, and held that when the State produces new evidence that the defendant lied under oath at the first trial, collateral es-toppel does not bar a subsequent perjury prosecution. The court found that this rule would bolster the policy considerations behind collateral estoppel, noting that

[o]n the one hand, there is a concern that allowing an acquittal to insulate the defendant from perjury will give a defendant “an uncontrollable license to testify falsely,” with a resulting detriment to the reliability of evidence. On the other hand, there is an apprehension that allowing a prosecution for perjury will give the state a “second shot” at defendant for the same wrong, or allow an overzealous prosecutor to use the perjury trial to retry issues already determined in defendant’s favor. The concern that the state should not be given a second chance based on the same evidence was central to the Court’s holding in Ashe. 5

At the perjury trial, the jury listened to a tape recording of Bolden’s confession, as well as to witnesses who testified about the confession, 6 and heard from three additional witnesses: (1) Dr. George McCormick, the coroner who performed the autopsy on Spicer, testified that she died of manual strangulation; (2) Rudeen Crawford, the owner of a gas station across from the storage warehouse where the murder was allegedly committed, testified that he saw a black man and white woman talking outside of the storage unit shortly before 6:00 p.m. on March 5, 1987; (3) Jim Gregory, a sergeant with the Monroe Police Department, testified that Spicer’s body was found in a trash dumpster on the Northeast Louisiana University campus, and stated that he obtained blood and hair samples from the storage unit floor. These three witnesses had testified at the Spicer murder trial.

The jury found Bolden guilty of perjury and he received the maximum sentence, ten years imprisonment at hard labor, to run consecutively with the Tennessee sentence. The Louisiana appellate court affirmed his conviction 7 and the state Supreme Court denied review. 8

On November 20, 1997, Bolden filed a § 2264 habeas corpus petition in federal district court asserting six grounds for relief, including a claim that the perjury trial violated the collateral estoppel component of the double jeopardy clause. The magistrate judge recommended, and the district court agreed, that the petition should be *583 denied. Specifically, the district court found, without mentioning the standard of review under the Antiterrorism and Effective Death Penalty Act (AEDPA), that Bolden’s double jeopardy rights were not violated because the jury could have found that the State failed to prove beyond a reasonable doubt that Bolden murdered Spicer without deciding whether his testimony was credible and without deciding whether Bolden in fact killed Spicer.

The district court granted a certificate of appealability on the only issue currently before the court, the double jeopardy claim.

ANALYSIS

Because Bolden’s § 2254 petition was filed on November 20, 1997, the AEDPA applies to this action. 9 As amended by the AEDPA, 28 U.S.C. § 2254(d) pertinently provides that:

(d) An application for a writ of habeas corpus on behalf of a person in custody pursuant to the judgment of a State court shall not be granted with respect to any claim that was adjudicated on the merits in State court proceedings unless the adjudication of the claim- — -

(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or

(2) resulted in a decision that 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).

Pure questions of law are reviewed under the “contrary to” standard, while pure questions of fact are reviewed under the “unreasonable determination of the facts” standard. 10 Bolden, however, raises mixed questions of law and fact which are reviewed under the “unreasonable application” standard. 11 An

application of law to facts is unreasonable only when it can be said that reasonable jurists considering the question would be of one view that the state court ruling was incorrect. In other words, we can grant habeas relief only if a state court decision is so clearly incorrect that it would not be debatable among reasonable jurists. 12

This standard of review is akin to the “clearly erroneous” standard. 13 Prior to the enactment of the AEDPA, however, pure questions of law and mixed questions of law and fact were reviewed de novo. 14

Central to the instant case, in Ashe v. Swenson the Supreme Court opined that the double jeopardy clause of the fifth amendment incorporates the collateral estoppel doctrine, which provides that “when an issue of ultimate fact has once been determined by a valid and final judgment, that issue cannot again be litigated between the same parties in any future lawsuit.” 15 In determining whether collateral estoppel bars subsequent crimi *584 nal prosecutions, we engage in a two-step analysis. Initially, we must decide which facts necessarily were decided in the first proceeding: Then we must consider whether the facts necessarily decided in the first trial constitute essential elements of the offense in the second trial. In criminal cases, collateral estoppel

is not to be applied with the hypertech-nical and archaic approach of a 19th century pleading book, but with realism and rationality. Where a previous judgment of acquittal was based upon a general verdict, as is usually the case, this approach requires a court to examine that record of a prior proceeding, taking into account the pleadings, evidence, charge, and other relevant matter, and conclude whether a rational jury could have grounded its verdict upon an issue other than that which the defendant seeks to foreclose from consideration. 16

Bolden first contends that his acquittal of Spicer’s murder necessarily determined that his statements that he did not kill Spicer or have physical contact with her were true, and thus would prevent a perjury conviction based upon those statements. He points to the prosecutor’s closing argument in which she specifically raised Bol-den’s credibility to the jury and notes that the State’s evidence was almost exclusively circumstantial. Bolden asserts that it ignores the reality of the trial to argue that the jury acquitted him, but did not believe his statements were true.

Second, Bolden argues that his acquittal also necessarily determined that he did not in fact murder Spicer. Accordingly, he contends that the determination of this fact negates an essential element of the perjury charge, that he made a false statement. Bolden asserts that to prove this element — that his statements that he did not kill Spicer or have physical contact with her were false — the State would have to relitigate the entire murder trial. Finally, Bolden contends that the newly obtained evidence, the confession, should be irrelevant to the determination whether collateral estoppel applies to this situation.

The State contends that the acquittal in the murder trial did not necessarily mean that the jury believed Bolden’s testimony; rather, the jury simply could have found that the State did not meet its burden of proof. The State also places great emphasis on Bolden’s subsequent confession, noting that it did not pursue Bolden and did not use the murder trial as a “dry run” for the perjury charges. Finally, the State maintains that a defendant who testifies falsely must suffer the consequences of that action, including conviction for perjury.

In this AEDPA habeas proceeding, we do not undertake a de novo review of the state court decisions. Instead, under the directives of Drinkard, we may only grant habeas relief if the Louisiana court’s ruling that collateral estoppel did not bar the perjury conviction was an unreasonable application of clearly established law as determined by the United States Supreme Court. Stated simply, we may proceed only if reasonable jurists would be of one mind that the Louisiana court’s ruling was incorrect.

To determine the facts necessarily decided in Bolden’s first trial under the first step of the collateral estoppel analysis, we must examine the elements of the statutes under which Bolden was charged. In Louisiana, second-degree murder is defined as “the killing of a human being ... [wjhen the offender has a specific intent to kill or to inflict great bodily harm.” 17 Perjury, on the other hand, is defined as the intentional making under oath of a false oral statement in a judicial proceed *585 ing, when the statement is material to an issue or question in controversy. 18

Both the Louisiana Supreme Court, in reviewing a pre-trial motion to quash the perjury charge, and the intermediate appellate court, on direct appeal of the perjury conviction, found that the veracity of Bolden’s statement and the inquiry whether Bolden murdered Spicer were not necessarily decided in the murder trial because the jury simply could have determined that the State did not prove its case beyond a reasonable doubt. We cannot say that this finding is an unreasonable application of clearly established federal law. We are keenly aware that every criminal case raising a collateral es-toppel challenge theoretically might seek to rely on this burden of proof proposition, an action that if not carefully applied could undermine and eventually defeat the purposes of the collateral estoppel doctrine. We emphasize that in this case, after reviewing the record, evidence, and charge as we are instructed to do by Ashe, we are persuaded beyond peradventure that the jury’s finding of reasonable doubt, and not the truthfulness of Bol-den’s statement or the conclusion that he did not murder Spicer, was the only issue necessarily determined by the acquittal on the murder charge. 19

As the Louisiana Supreme Court noted, at the murder trial the State produced no eyewitnesses, presented only inconclusive physical evidence, and included some evidence of motive and opportunity, countered, however, by alibi evidence of the defendant’s attendance at the basketball game. Based upon the entire record and surrounding circumstances, we agree with the state court’s finding that the murder trial jury very likely could have based its verdict on issues other than those presented in the perjury trial. At the very minimum, reasonable jurists would not be of one mind that this ruling was incorrect. 20 Further, under the second step of the collateral estoppel analysis, the fact necessarily decided in the murder trial was not an essential element of the perjury trial.

We conclude that the state court decision finding that collateral estoppel did not bar Bolden’s perjury prosecution was not an unreasonable application of federal law. *586 Accordingly, the district court’s denial of § 2254 relief was not in error.

The judgment appealed is AFFIRMED.

. State v. Bolden, 639 So.2d 721 (La.1994).

. State v. Bolden, 680 So.2d 6 (La.App.1996).

. On April 23, 1991, Bolden gave a statement to New Jersey police in part as follows:

Q. What were the circumstances surrounding the death of Ms. Spicer?

A. I went, um, I asked her come to like, we had a storage unit, and I asked her to come there with me and then I was trying to talk to her, you know, I had been asking her and asking her to, you know, try to give me some time with Joel and she just, you know, she just kept saying that she was going to be with Joel no matter what, and so I just, I got mad with her and I strangled her.

Q. And where did this take place at, the storage area?

A. Yeah.

Q. And where was the storage area located?

A. Not far from the college campus in Monroe, Louisiana.

Q. And after you strangled her, what did you do?

A. Took her body back to the campus and put it in the dumpster and went back to the game or I went back to the dorm or something.

. Bolden, 639 So.2d at 725 (citations omitted).

. Id. at 726 (citing Ashe v. Swenson, 397 U.S. 436, 90 S.Ct. 1189, 25 L.Ed.2d 469 (1970), other citations omitted). In footnote five of its opinion, the Louisiana Supreme Court noted that under state law Bolden's unsworn statement to police may, by itself, be insufficient to convict him of perjury and stated that at trial the State would have to produce corroborating evidence to demonstrate that his New Jersey confession was truthful. Id. at 726 n. 5.

. New Jersey officers Captain Robert Scara, Captain Michael King, and Sergeant Cook testified that Bolden was read and waived his rights, and that Bolden was not threatened or coerced into making his statement.

. State v. Bolden, 680 So.2d 6 (La.App.1996).

. State v. Bolden, 683 So.2d 286 (La. 1996).

. See Lindh v. Murphy, 521 U.S. 320, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997).

. Drinkard v. Johnson, 97 F.3d 751, 767-68 (5th Cir.1996).

. Id.

. Id. at 769 (emphasis in original).

. Mata v. Johnson, 99 F.3d 1261, 1267 (5th Cir.1996), vacated in part on reh’g, 105 F.3d 209 (5th Cir.1997).

. Johnson v. Puckett, 176 F.3d 809 (5lh Cir.1999), reh’g and reh’g en banc denied, 184 F.3d 820 (5lh Cir.1999). We note with concern that neither party nor the district court cited Drinkard or the standard of review under the AEDPA. We emphasize that under the AEDPA’s deferential review scheme, it is essential for arguments and decisions to give due focus to the appropriate standard of review.

. Ashe v. Swenson, 397 U.S. 436, 443, 90 S.Ct. 1189, 25 L.Ed.2d 469 (1970).

. Id. at 444, 90 S.Ct. 1189 (internal quotation marks omitted).

. La.Rev.Stat.§ 14:30.1.

. La.Rev.Stat. § 14:123.

. The State does not offer the persuasive contention that, because second degree murder requires a specific intent to kill or inflict great bodily harm, the jury could have based its acquittal on a finding of no intent, rather than a finding that Bolden did not kill Spicer. This proposition supports our conclusion that the truthfulness of Bolden's statements and whether he killed Spicer were not necessarily determined in the first trial.

. Because of today’s disposition, we are not required to reach the question of the Louisiana Supreme Court's alternative adoption of the "new and additional evidence” exception to later perjury prosecutions, but opt to address this issue for the sake of completeness. In Bolden, the court decided that, even if a jury necessarily determined in the first trial issues raised by the second prosecution, collateral estoppel would not bar a subsequent perjury prosecution if new and additional evidence obtained after the original trial proved beyond a reasonable doubt that the defendant lied under oath. State v. Bolden, 639 So.2d 721, 725-26 (La.1994).

Posing a purely legal question, the adoption of this exception would be judged under the AEDPA's "contrary to” standard. See Drinkard, 97 F.3d at 767-68. Were we to decide this issue, we would find that this exception is not "contrary to” federal law as established by the Supreme Court.

A primary concern of the Supreme Court in Ashe was the prosecution's use of the first trial as a “dry run” for the second prosecution. Ashe, 397 U.S. at 447, 90 S.Ct. 1189. When new and additional evidence of perjury is obtained in good faith, as was done in this case, the "dry run” concern is not present. Furthermore, as the Louisiana Supreme Court noted, this rule balances the concern that the prosecution will get a "second shot” at the defendant with the concern that the defendant will have an "uncontrollable license” to testify falsely at the first trial, without fear of repercussions. Bolden, 639 So.2d at 726. Further, this rule is bolstered by the Supreme Court's holding that criminal defendants do not have a constitutional right to testify falsely. See Nix, v. Whiteside, 475 U.S. 157, 106 S.Ct. 988, 89 L.Ed.2d 123 (1986).