PER CURIAM.
The petitioner, Duane Passino, appeals from the denial of his request for issuance of a writ of habeas corpus. Before this court, he asserts that the state trial court committed reversible error in allowing the prosecutor to ask a government witness at trial whether the witness understood he could be required, as a condition of a plea agreement, to submit to a polygraph examination. According to Passino, such questioning before a jury amounted to improper bolstering of the credibility of a material witness. Because we agree that the state court’s determination that any error in this regard was harmless is itself an objectively reasonable application of Supreme Court law, we affirm the judgment of the district court.
FACTUAL AND PROCEDURAL BACKGROUND
Passino was convicted in Michigan state court of three violations of that state’s drug laws and sentenced to an effective prison term of 20-40 years. During the state court trial, numerous witnesses testified on behalf of the prosecution regarding their personal drug dealings with Passino [125]*125or concerning their knowledge of such illicit activity involving the petitioner. Given the fact that the credibility of the testifying witnesses would thus be crucial to the efforts of the state to obtain criminal convictions in this matter, the prosecutor questioned one witness on redirect examination as follows:
Q Mr. Couture, you have no prior criminal record—felony record?
A No.
Q And you agreed to testify truthfully, not only under oath at the grand jury, but other proceedings, is that correct?
A Yes.
Q And you were given to understand that at any time you could be required to take a polygraph for part of any testimony concerned?
A Yes.
At the close of the questioning, defense counsel interposed an objection, claiming that the line of inquiry “was a deliberate attempt to inject into the record reference to polygraphs, to bolster testimony which may be questionable in the eyes of the jury.” The trial judge denied the motion for mistrial, however, and the jury concluded that the government had established its case against Passino beyond a reasonable doubt.
State court review of the convictions also failed to provide Passino with the relief he sought. The Michigan Court of Appeals did conclude that the trial court decision to admit into evidence the testimony concerning the polygraph examination was error. That appellate court further determined, however, that any such error was harmless beyond a reasonable doubt. In doing so, the court stated:
We first note that the prosecutor never argued, much less argued repeatedly, that Couture had testified truthfully because of the plea agreement. Thus, although the prosecutor initially erred, he did not prejudice defendant by vouching for Couture’s credibility.... Moreover, the fleeting reference to the requirement of a polygraph exam in the plea agreement did not imply that the prosecution possessed special knowledge, unknown to the jury, that the witness was testifying truthfully. Nevertheless, we caution prosecutors not to use such plea agreements as a back door method of injecting evidence that a witness has agreed to submit to a polygraph examination. A prosecutor’s attempt to use the threat of a polygraph examination as a means of bolstering a witness’ testimony, or vouching for his or her credibility, is error.
The Michigan Supreme Court declined to review the matter further, eventually leading the petitioner to seek habeas corpus relief.
Both a magistrate judge and the federal district court found no merit to the issues raised by Passino on collateral review and denied the petition in its entirety. Although the district court refused to grant the petitioner a certificate of appealability on any of the alleged grounds for relief, we granted Passino the right to address on appeal the question whether the petitioner was “denied a fair trial when the prosecutor asked witness Michael Couture whether he understood that he could be required to submit to a polygraph examination.” Only that issue is therefore now before us for resolution.
DISCUSSION
Passino filed his petition for issuance of the writ of habeas corpus on June 19,1998, well after the April 24, 1996 effective date of the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA), Pub. L. No. 104-132, 110 Stat. 1214 (1996). Conse[126]*126quently, the provisions of that act govern the resolution of this controversy. See Lindh v. Murphy, 521 U.S. 320, 336, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997); Greer v. Mitchell, 264 F.3d 663, 671 (6th Cir. 2001), cert. denied, 535 U.S. 940, 122 S.Ct. 1323, 152 L.Ed.2d 231 (2002). Pursuant to that legislation, a federal court may not grant the writ unless the state court adjudication on the merits either:
(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 upon an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.
28 U.S.C. § 2254(d).
As explained by the United States Supreme Court:
Under the “contrary to” clause, a federal habeas court may grant the writ if the state court arrives at a conclusion opposite to that reached by this Court on a question of law or if the state court decides a case differently than this Court has on a set of materially indistinguishable facts. Under the “unreasonable application” clause, a federal habeas court may grant the writ if the state court identifies the correct governing legal principle from this Court’s decisions but unreasonably applies that principle to the facts of the prisoner’s case.
Williams v. Taylor, 529 U.S. 362, 412-13, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). In deciding whether a state court ruling involved an “unreasonable application” of federal law, a habeas court does not focus merely upon whether the state court decision was erroneous or incorrect; rather, a federal court may issue a writ of habeas corpus only if the state court’s application of clearly-established federal law was objectively unreasonable. See id. at 409-11. “This court reviews a district court’s legal conclusions de novo and its factual findings for clear error.” Greer, 264 F.3d at 671 (citing Lucas v. O’Dea, 179 F.3d 412, 416 (6th Cir.1999)).
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PER CURIAM.
The petitioner, Duane Passino, appeals from the denial of his request for issuance of a writ of habeas corpus. Before this court, he asserts that the state trial court committed reversible error in allowing the prosecutor to ask a government witness at trial whether the witness understood he could be required, as a condition of a plea agreement, to submit to a polygraph examination. According to Passino, such questioning before a jury amounted to improper bolstering of the credibility of a material witness. Because we agree that the state court’s determination that any error in this regard was harmless is itself an objectively reasonable application of Supreme Court law, we affirm the judgment of the district court.
FACTUAL AND PROCEDURAL BACKGROUND
Passino was convicted in Michigan state court of three violations of that state’s drug laws and sentenced to an effective prison term of 20-40 years. During the state court trial, numerous witnesses testified on behalf of the prosecution regarding their personal drug dealings with Passino [125]*125or concerning their knowledge of such illicit activity involving the petitioner. Given the fact that the credibility of the testifying witnesses would thus be crucial to the efforts of the state to obtain criminal convictions in this matter, the prosecutor questioned one witness on redirect examination as follows:
Q Mr. Couture, you have no prior criminal record—felony record?
A No.
Q And you agreed to testify truthfully, not only under oath at the grand jury, but other proceedings, is that correct?
A Yes.
Q And you were given to understand that at any time you could be required to take a polygraph for part of any testimony concerned?
A Yes.
At the close of the questioning, defense counsel interposed an objection, claiming that the line of inquiry “was a deliberate attempt to inject into the record reference to polygraphs, to bolster testimony which may be questionable in the eyes of the jury.” The trial judge denied the motion for mistrial, however, and the jury concluded that the government had established its case against Passino beyond a reasonable doubt.
State court review of the convictions also failed to provide Passino with the relief he sought. The Michigan Court of Appeals did conclude that the trial court decision to admit into evidence the testimony concerning the polygraph examination was error. That appellate court further determined, however, that any such error was harmless beyond a reasonable doubt. In doing so, the court stated:
We first note that the prosecutor never argued, much less argued repeatedly, that Couture had testified truthfully because of the plea agreement. Thus, although the prosecutor initially erred, he did not prejudice defendant by vouching for Couture’s credibility.... Moreover, the fleeting reference to the requirement of a polygraph exam in the plea agreement did not imply that the prosecution possessed special knowledge, unknown to the jury, that the witness was testifying truthfully. Nevertheless, we caution prosecutors not to use such plea agreements as a back door method of injecting evidence that a witness has agreed to submit to a polygraph examination. A prosecutor’s attempt to use the threat of a polygraph examination as a means of bolstering a witness’ testimony, or vouching for his or her credibility, is error.
The Michigan Supreme Court declined to review the matter further, eventually leading the petitioner to seek habeas corpus relief.
Both a magistrate judge and the federal district court found no merit to the issues raised by Passino on collateral review and denied the petition in its entirety. Although the district court refused to grant the petitioner a certificate of appealability on any of the alleged grounds for relief, we granted Passino the right to address on appeal the question whether the petitioner was “denied a fair trial when the prosecutor asked witness Michael Couture whether he understood that he could be required to submit to a polygraph examination.” Only that issue is therefore now before us for resolution.
DISCUSSION
Passino filed his petition for issuance of the writ of habeas corpus on June 19,1998, well after the April 24, 1996 effective date of the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA), Pub. L. No. 104-132, 110 Stat. 1214 (1996). Conse[126]*126quently, the provisions of that act govern the resolution of this controversy. See Lindh v. Murphy, 521 U.S. 320, 336, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997); Greer v. Mitchell, 264 F.3d 663, 671 (6th Cir. 2001), cert. denied, 535 U.S. 940, 122 S.Ct. 1323, 152 L.Ed.2d 231 (2002). Pursuant to that legislation, a federal court may not grant the writ unless the state court adjudication on the merits either:
(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 upon an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.
28 U.S.C. § 2254(d).
As explained by the United States Supreme Court:
Under the “contrary to” clause, a federal habeas court may grant the writ if the state court arrives at a conclusion opposite to that reached by this Court on a question of law or if the state court decides a case differently than this Court has on a set of materially indistinguishable facts. Under the “unreasonable application” clause, a federal habeas court may grant the writ if the state court identifies the correct governing legal principle from this Court’s decisions but unreasonably applies that principle to the facts of the prisoner’s case.
Williams v. Taylor, 529 U.S. 362, 412-13, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). In deciding whether a state court ruling involved an “unreasonable application” of federal law, a habeas court does not focus merely upon whether the state court decision was erroneous or incorrect; rather, a federal court may issue a writ of habeas corpus only if the state court’s application of clearly-established federal law was objectively unreasonable. See id. at 409-11. “This court reviews a district court’s legal conclusions de novo and its factual findings for clear error.” Greer, 264 F.3d at 671 (citing Lucas v. O’Dea, 179 F.3d 412, 416 (6th Cir.1999)).
In Passino’s case, the Michigan Court of Appeals determined that the trial judge erred in allowing the prosecution to bolster the testimony of one of its witnesses by intimating that the witness’s statements were worthy of belief because of a prior agreement to be available for a polygraph examination. Improper “[bjolstering occurs when the prosecutor implies that the witness’s testimony is corroborated by evidence known to the government but not known to the jury.” United States v. Francis, 170 F.3d 546, 551 (6th Cir.1999) (citing United States v. Sanchez, 118 F.3d 192, 198 (4th Cir.1997)). By mentioning before the jury that Couture had agreed to submit to polygraph examinations regarding his trial testimony, the prosecutor not only suggested that Couture should be believed because of his truthfulness, but also improperly vouched for the reliability of lie detector tests themselves. As recognized by the United States Court of Appeals for the Ninth Circuit in a somewhat analogous case:
[T]he plea-bargain agreement, like a covenant of faith, told [the jury] that the prosecution stood ready at all stages to bring the witnesses to account should they stray from the truth. It gave assurance not only that the witnesses were truthful when the prosecution decided to put them on the stand, but also that their revelations to the jury could be believed because of the threat of certain exposure. That resource, like a bright line to honesty, suggests that the scientific apparatus can tell the difference. It also opens the intimation that the Government knows that its witnesses have told and are telling the truth because otherwise they would not have been offered as witnesses. Further, the jury [127]*127may be led to think that should their jury testimony later be found false even after leaving the witness stand, the Government surely would know and surely would act to purge any falsity from the record.
United States v. Brown, 720 F.2d 1059, 1074 (9th Cir.1983).
Despite “generally disfavor[ing] admitting the results of polygraph examinations,” United States v. Thomas, 167 F.3d 299, 308 (6th Cir.1999), we have, nevertheless, “refused to impose a per se prohibition against polygraph evidence, and the mere mention of the words ‘polygraph examination’ does not entitle a defendant to a new trial.” United States v. Odom, 13 F.3d 949, 957 (6th Cir.1994). Other decisions from this court, however, indicate that admission of testimony regarding the results of polygraph examinations is erroneous simply because such testimony is inherently unreliable. See King v. Trippett, 192 F.3d 517, 523-24 (6th Cir.1999) (citing United States v. Scheffer, 523 U.S. 303, 118 S.Ct. 1261, 140 L.Ed.2d 413 (1998)); United States v. Scarborough, 43 F.3d 1021, 1026 (6th Cir.1994).
Nevertheless, even a determination of error in the prosecutor’s reference to the polygraph examination is not sufficient by itself to justify an award of relief in this case. The district court and the Michigan Court of Appeals, after recognizing the trial court’s error, each concluded that any error was harmless beyond a reasonable doubt and did not have “a substantial and injurious effect or influence in determining the jury’s verdict.” Brecht v. Abrahamson, 507 U.S. 619, 637, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993). Not only did the question propounded by the prosecutor not request information on the results of any polygraph examination, the reference to such a test was confined to that single instance and the additional evidence adduced against the petitioner clearly implicated him in the crimes for which he was indicted and ultimately convicted.
Most importantly, the state need not establish definitively that any error in this regard was harmless. Instead, the writ will not issue unless the petitioner can establish that the Michigan Court of Appeals’s determination was objectively unreasonable. Without question, given the rationale offered by the state court to support its conclusion in this case, it is at least “reasonable” for a state court to find that an error as isolated as that committed during Passino’s trial did not affect the ultimate result reached in that prosecution.
CONCLUSION
For the reasons set out above, we AFFIRM the judgment of the district court.