Petitioner-Appellant Jonathan Robbins appeals the district court’s dismissal of his petition for a writ of habeas corpus. For the reasons discussed below, we AFFIRM the dismissal of the petition.
I. BACKGROUND
On March 9, 1993, a jury found Robbins guilty on five counts of permitting drug abuse, in violation of O.R.C. § 2925.13; three counts of complicity to aggravated trafficking in drugs, in violation of O.R.C. § 2923.03(A)(1); and one count of aggravated trafficking in drugs, in violation of O.R.C. § 2925.03(A)(1). Robbins appealed, and the judgment of the trial court was affirmed. The Ohio Supreme Court then denied leave to appeal.
Robbins then filed a delayed application for reopening of his appeal pursuant to Ohio Appellate Rule 26(B). The motion was granted and new appellate counsel appointed. On June 12, 1996, the reopening of the appeal was denied and the trial court judgment affirmed. The Ohio Supreme Court again denied review. Robbins then filed a second application for reopening of his first appeal pursuant to Rule 26(B), which was denied. The Ohio Supreme Court once again denied review.
On September 14, 1996, Robbins filed a petition for post-conviction relief or, in the alternative, a motion for a new trial based on newly discovered evidence, which the trial court denied. The appellate court affirmed, and the Ohio Supreme Court denied review.
Robbins filed a second petition for post-conviction relief based on new evidence on December 16, 1996, which the trial court denied. The Fifth District Court of Appeals reversed and remanded the case to the trial court. The trial court again denied relief, and this time the appellate court affirmed. The Ohio Supreme Court dismissed the appeal.
On November 18, 1998, Robbins filed a petition for a writ of habeas corpus pro se in the United States District Court for the Northern District of Ohio, pursuant to 28 *382U.S.C. § 2254. On December 4, 1998, the case was transferred to the Southern District of Ohio, Judge John D. Holschuh.
In his habeas petition, Robbins asserted that he was denied the right to the effective assistance of appellate counsel, in violation of the Sixth and Fourteenth Amendments. Robbins’ claims regarding his appellate counsel relate back to his trial, which he believes was unfair for two reasons. First, Robbins objected to his trial counsel’s handling of the testimony of a government informant, who was working under a contract agreement with the police. Despite the dubiousness of the informant’s testimony, Robbins’ trial counsel failed to obtain a cautionary instruction regarding the informant’s credibility. Trial counsel also did not object to the prosecutor’s failure to introduce into evidence the contract between the informant and the police. Second, Robbins also objected to trial counsel’s failure to subpoena Robbins’ co-defendant, whom he regarded as an important exculpatory witness, to testify on his behalf.
Robbins asserted in his habeas petition that his counsel during the Rule 26(B) proceedings (hereinafter “Murnahan counsel”1) was ineffective because counsel failed to raise, during those proceedings, the ineffective assistance of direct appellate counsel in failing to raise trial counsel’s ineffective assistance regarding the informant. See J.A. at 884. Robbins also asserted the ineffective assistance of his direct appellate counsel for failing to raise on direct appeal trial counsel’s ineffectiveness regarding the informant. See id. at 895.
The district court concluded that Robbins had established deficient performance of his Murnahan counsel. See J.A. at 886-87. However, the district court also found that trial counsel’s failure to request a special cautionary instruction on the reliability of the informant’s testimony and Mumahan counsel’s failure to raise the issue on appeal did not undermine the reliability of the trial or deprive Robbins of a fair trial. See J.A. at 895. The district court also concluded that Robbins had procedurally defaulted two of his claims regarding the informant’s testimony, and that Robbins failed to establish as a required cause for such default the ineffective assistance of his direct appellate counsel. See J.A. at 897-98. Finally, the district court also concluded that Robbins had failed to establish the ineffective assistance of his trial counsel for failing to subpoena Robbins’ co-defendant to testify for the defense. See J.A. at 906. Accordingly, the district court dismissed Robbins’ habeas petition. See id.
In this appeal, Robbins raises three issues. First, he claims that the district court erred in concluding that he was not denied the effective assistance of appellate counsel for failing to raise the ineffective assistance of trial counsel regarding the testimony of the informant. Pro Se Appellant’s Brief at 1. Second, Robbins claims that the district court erred in concluding that he was not denied the effective assistance of trial counsel based on trial counsel’s failure to subpoena Robbins’ co-defendant to testify on his behalf. Id. Third, Robbins claims that the district court erred in holding that he had procedurally defaulted two of his claims, and had failed to establish cause to overcome these defaults. Id.
II. ANALYSIS
A. Standard of Review
The disposition of a habeas petition by the district court is reviewed de novo. *383Bronaugh v. Ohio, 235 F.3d 280, 282 (6th Cir.2000). The factual findings of a district court are reviewed under a clearly erroneous standard. Lucas v. O’Dea, 179 F.3d 412, 416 (6th Cir.1999).
Because the petition for a writ of habeas corpus in this case was filed in the district court after April 24, 1996, this Court’s review of the state trial and appellate court decisions is governed by the Antiterrorism and Effective Death Penalty Act of 1996, Pub.L. No. 104-132, 100 Stat. 1214 (1996). Williams v. Taylor, 529 U.S. 362, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000); Lindh v. Murphy, 521 U.S. 320, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997); Harpster v. Ohio, 128 F.3d 322, 326 (6th Cir.1997), cert denied, 522 U.S. 1112, 118 S.Ct. 1044, 140 L.Ed.2d 109 (1998).
Under that statute, this Court may not issue the writ of habeas corpus to reverse either the state trial or appellate court decision 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).
B. Analysis of the Three Issues Robbins Raises on Appeal
1. Whether the district court erred in concluding that Robbins was not denied the effective assistance of appellate counsel for failing to raise the ineffective assistance of trial counsel regarding the testimony of the informant.
Robbins maintains that his trial counsel should have objected to both the prosecutor’s failure to introduce the government contract under which the informant testified against Robbins, and to the informant’s testimony as unduly coercive and in violation of due process. Robbins also claims that trial counsel should have requested a special cautionary instruction regarding the credibility of the informant. Robbins further claims that his appellate counsel’s failure to raise these instances of what Robbins considers ineffective assistance of trial counsel amounts to ineffective assistance of appellate counsel.
We begin with the standard for ineffective assistance of counsel:
A convicted defendant’s claim that counsel’s assistance was so defective as to require reversal of a conviction or death sentence has two components. First, the defendant must show that counsel’s performance was deficient. This requires showing that counsel ... was not functioning as the “counsel” guaranteed the defendant by the Sixth Amendment. Second, the defendant must show that the deficient performance prejudiced the defense. This requires that counsel’s errors were so serious as to deprive the defendant of a fair trial, a trial whose result is rehable. Unless a defendant makes both showings, it cannot be said that the conviction or death sentence resulted from a breakdown in the adversary process that renders the result unreliable.
Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). If the Court determines that the petitioner has failed to satisfy one prong of the Strickland test, it need not consider the other. Strickland, 466 U.S. at 697.
“Because of the difficulties inherent in making the evaluation, a court must in*384dulge a strong presumption that counsel’s conduct falls within the wide range of reasonable professional assistance; that is, the defendant must overcome the presumption that, under the circumstances, the challenged action might be considered sound trial strategy.” Strickland, 466 U.S. at 689.
To establish prejudice, it must be shown that there is a reasonable probability that, but for counsel’s errors, the result of the proceedings would have been different. Strickland, 466 U.S. at 694. “A reasonable probability is a probability sufficient to undermine confidence in the outcome.” Id.
The district court found that Robbins failed to establish ineffective assistance of trial counsel based on her failure to object to the non-introduction of the informant’s contract with the government. The district court discussed and distinguished an Eighth Circuit case that considered an agreement between the government and a prosecution witness. In United States v. Waterman, 732 F.2d 1527 (8th Cir.1984), the Eighth Circuit stated that “the government cannot consistent with due process offer favorable treatment to a prosecution witness contingent upon the success of the prosecution.” 732 F.2d at 1531. The district court pointed out that while Waterman speaks of an agreement contingent upon the success of the prosecution, the agreement in this case only speaks of the pursuance of a prosecution or arrest. The incentive in the informant’s agreement in this ease was based on the arrest or prosecution of Robbins, which had already occurred when the informant testified. The agreement here simply did not require the quality of information that the agreement in Waterman required. Furthermore, because the contract in this case was read to the jury, it is difficult to say that trial counsel’s failure to request its introduction amounted to an error “so serious as to deprive the defendant of a fair trial.” Strickland, 466 U.S. at 687. Therefore, we agree with the district court that Robbins has failed to establish ineffective assistance of trial counsel based on her failure to object to the non-introduction of the informant’s agreement with the government.
The district court also rejected Robbins’ claim that his trial counsel was ineffective for failing to object to the informant’s testimony as unduly coercive and in violation of due process. This Circuit specifically allows informants to testify under agreements with the government that provide incentives for the informant’s testimony. See United States v. Grimes, 438 F.2d 391, 395 (6th Cir.1971). Here, the informant’s testimony was corroborated to some extent by tape recordings and police testimony. Furthermore, defense counsel rigorously cross-examined the informant. Finally, the incentive in the agreement was based on the arrest or prosecution of Robbins, which had already occurred by the time the informant took the stand. For these reasons, we agree with the district court that Robbins’ trial counsel was not ineffective for failing to object to the informant’s testimony.
Finally, the district court also rejected Robbins’ claim that trial counsel was ineffective for failing to request a special cautionary instruction regarding the credibility of the informant. Again, the informant’s testimony was corroborated, and he was rigorously cross-examined by defense counsel. Furthermore, although no special cautionary instruction was given, the trial court instructed the jury that they did not have to believe any witness testimony, and that they should judge each witness’ credibility exactingly. See J.A. at 893-94. Although a special cautionary instruction may have been pref*385erable in light of the informant’s agreement with the government, the jury was clearly on notice that it was to scrutinize the credibility of each witness. Again, we cannot say that any error in this regard was “so serious as to deprive the defendant of a fair trial.” Strickland, 466 U.S. at 687.
There is a right to effective assistance of counsel in connection with a defendant’s first appeal of right. Evitts v. Lucey, 469 U.S. 387, 396, 105 S.Ct. 830, 83 L.Ed.2d 821 (1985). However, it is not necessary for appellate counsel to raise every non-frivolous claim on direct appeal. Jones v. Barnes, 463 U.S. 745, 103 S.Ct. 3308, 77 L.Ed.2d 987 (1983). In fact, the process of “winnowing out weaker arguments on appeal” is “the hallmark of effective appellate advocacy.” Smith v. Murray, 477 U.S. 527, 536, 106 S.Ct. 2661, 91 L.Ed.2d 434 (1986) (internal quotations and citations omitted). “Generally, only when ignored issues are clearly stronger than those presented, will the presumption of effective assistance of counsel be overcome.” Gray v. Greer, 800 F.2d 644, 646 (7th Cir.1986).
Here, Robbins was not denied his right to the effective assistance of appellate counsel. His arguments based on trial counsel’s alleged ineffectiveness regarding the informant’s testimony were weak and, ultimately, unpersuasive. Appellate counsel’s failure to raise them therefore cannot amount to ineffective assistance.
2. Whether the district court erred in concluding that Robbins was not denied the effective assistance of trial counsel based on her failure to subpoena his co-defendant to testify on Robbins’ behalf
Robbins also argues that his trial counsel was ineffective for failing to call his co-defendant, Joseph Smith, as a defense witness at trial. Robbins’ petition for post-conviction relief included an affidavit in which Smith stated that he was present when the alleged drug transactions took place, and that he had informed Robbins’ trial counsel that he could testify as to Robbins’ innocence. See J.A. at 904. An evidentiary hearing was held, at which trial counsel stated that she had no recollection of any conversation with Smith, and that if Smith had informed her that he was willing to assist in Robbins’ defense, she would have subpoenaed him for trial. See id. As trial counsel recalled, Robbins and Smith had “pointed the finger” at each other. See id. Dismissing Smith’s affidavit as “incredible” and apparently believing trial counsel’s account, the state appellate court rejected Robbins’ claim of ineffective assistance. See id. Reviewing that record, the district court concluded that Robbins had failed to establish the ineffective assistance of his trial counsel regarding Smith under either prong of the Strickland test.
We agree with the district court. Given trial counsel’s recollection that the two defendants were “pointing fingers” at each other, the determination not to call Smith might have been “sound trial strategy.” Trial counsel also recalled that Robbins was actively involved in the preparation of his defense and provided a witness list, which was investigated. See J.A. at 30. In sum, the information on which the state appellate court and the district court relied supports, rather than rebuts, the presumption that trial counsel’s conduct fell “within the wide range of reasonable professional assistance.” Strickland, 466 U.S. at 689.
3. Whether the district court erred in holding that Robbins procedurally defaulted two of his claims and had failed to establish cause to overcome those defaults.
In an Opinion and Order dated December 6, 1999, the district court concluded *386that Robbins had waived his right to present two of his claims for federal habeas review. See J.A. at 878. Robbins asserted as cause for his procedural default the ineffective assistance of his second appellate attorney, appointed for purposes of pursuing Robbins’ first delayed application for reopening of his appeal.
The district court noted that this Circuit recently held that an application for reopening of an appeal pursuant to Ohio Appellate Rule 26(B) (the so-called Murnahan motion) is part of the direct appeal process, such that a defendant represented by counsel in such a proceeding has a right to effective assistance. White v. Schotten, 201 F.3d 743, 752-53 (6th Cir.2000). As discussed above, the district court concluded that Robbins had established deficient performance of his Murnahan counsel. See J.A. at 886-87. However, the district court found that Robbins had failed to establish prejudice under the second prong of the Strickland test. See J.A. at 895.
The two claims on which Robbins procedurally defaulted are similar, if not identical, to arguments considered earlier in this opinion. The first defaulted claim alleged a denial of effective assistance of direct appellate counsel for failing to raise the issue of ineffective assistance of trial counsel based on trial counsel’s failure to request a cautionary instruction on the informant’s testimony. The second defaulted claim alleged a denial of effective assistance of direct appellate counsel for failure to object to the prosecutor’s exclusion of the contract between the government and the informant.
As discussed above, neither the lack of a cautionary instruction regarding the informant’s testimony, nor the exclusion from evidence of the contract between the informant and the government, amounted to an error so serious as to undermine the reliability of the result or deny Robbins a fair trial. Therefore, we agree with the district court that, even though the performance of Robbins’ Murnahan counsel may have been deficient, the deficiency did not prejudice the outcome of the proceedings.
III. CONCLUSION
For the foregoing reasons, the judgment of the district court is AFFIRMED.
. In State v. Murnahan, 63 Ohio St.3d 60, 584 N.E.2d 1204 (Ohio 1992), the Ohio Supreme Court first identified Rule 26(B) as the vehicle for raising claims of ineffective assistance of counsel on direct appeal.