ORDER DENYING CERTIFICATE OF APPEALABILITY *
Michael Villareal seeks a certificate of appealability (COA) to challenge the district court’s denial of his petition for a writ of habeas corpus filed under 28 U.S.C. § 2254.
His petition presented three challenges to a 2009 conviction in Oklahoma state court of lewd molestation of two young girls. First, Villareal argued that the trial court violated his right to due process when it allowed a victim of a prior crime to testify to her encounters with Villareal. Second, Villareal asserted that the admission of evidence relating to a fourth victim from a prior crime violated the collateral estoppel component of the Double Jeopardy Clause because he had been acquitted of the charges relating to that victim. Third, Villareal argued that he was denied his Sixth Amendment right to effective assistance of trial counsel because of his attorney’s failure to object to the testimony and arguments concerning the fourth victim. In addition, Villareal’s application to this court raised a cumulative error argument that he did not present below.
Exercising jurisdiction under 28 U.S.C. §§ 1291 and 2253, we deny a COA and dismiss the appeal.
I. Background
An Oklahoma state court jury convicted Michael Villareal of lewd molestation of two young girls, J.Y. and her cousin M.C. Both J.Y. and M.C. testified at the trial, as did a third girl, E.J., who testified that Villareal had sexually abused her several years earlier. Prior to trial, the state filed a Notice of Intent to Offer Evidence of Other Crimes which detailed E.J.’s allegations alongside those of a fourth girl, M.O. After Villareal objected and a hearing was held, the trial court excluded the evidence relating to M.O. but ruled that the allegations by E.J. would be admissible.
At trial, J.Y. and M.C. testified that Villareal began abusing them at five and nine years old, respectively, while he was living with J.Y.’s mother. J.Y. further testified that Villareal ensured her silence by threatening to kill her animals if she told anyone about the abuse. E.J. provided similar testimony — she asserted that Villa-*593real had abused her beginning when she was seven years old while Villareal was living with E.J. and her mother. She further testified that Villareal threatened to beat her brother if she told anyone about the abuse. On cross-examination, Villareal’s attorney attempted to impeach E.J.’s credibility by questioning why she had not told anyone about the abuse earlier. During that line of questioning, the following exchange occurred:
Q: Did you ever tell anyone else?
A: I told a friend.
Q: Did that friend go to the cops?
A: Yes, she did.
R., Vol. II, Doc. 13-1 at 186. The prosecutor, believing the door had been opened to testimony concerning the friend, established on re-direct that the friend in question was M.O., that M.O. went to the police about her own abuse at the hands of Villa-real, and that M.O. also came from a single-parent household. Although the jury was not informed of the fact, Villareal earlier had been tried and acquitted of molestation charges relating to M.O.
Villareal raised three issues on direct appeal, all of which he subsequently raised in his petition for a writ of habeas corpus in federal court. He raises each of these issues again in his application for a COA and also advances a cumulative error argument not presented below.
II. Analysis
A COA is a jurisdictional prerequisite to our review of a § 2254 action. Clark v. Oklahoma, 468 F.3d 711, 713 (10th Cir.2006). “We will issue a COA ‘only if the applicant has made a substantial showing of the denial of a constitutional right.’” Allen v. Zavaras, 568 F.3d 1197, 1199 (10th Cir.2009) (quoting Miller-El v. Cockrell, 537 U.S. 322, 336, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003)). A “substantial showing” requires that the movant demonstrate “that reasonable jurists could debate whether (or, for that matter, agree that) the petition should have been resolved in a different manner or that the issues presented were adequate to deserve encouragement to proceed further.” Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000). We conduct this review against the background of the Antiterrorism and Effective Death Penalty Act, which prohibits us from overturning a state’s adjudication of a claim unless it is “contrary to, or involved an unreasonable application of, clearly established Federal law.” 28 U.S.C. § 2254(d); Dockins v. Hines, 374 F.3d 935, 938 (10th Cir.2004). As for the order below, “we review the district' court’s legal conclusions de novo and its factual findings under the clearly erroneous standard.” English v. Cody, 241 F.3d 1279, 1282 (10th Cir.2001) (internal quotation marks omitted).
A. Admission of EJ.’s Testimony
Villareal first argues that the district court violated his right to due process by allowing E.J. to testify that he had abused her years earlier. Because the habeas statute only allows for a writ of habeas corpus to issue to a state prisoner who is “in custody in violation of the Constitution or laws or treaties of the United States,” 28 U.S.C. § 2254(a), we do not consider whether the trial court committed an error of state law by admitting E.J.’s testimony, see Estelle v. McGuire, 502 U.S. 62, 67, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991). Rather, we may only “disturb a state court’s admission of evidence of prior crimes, wrongs or acts” if “the probative value of such evidence is so greatly outweighed by the prejudice flowing from its admission that the admission denies [the] defendant due process of law.” Knighton v. Mullin, 293 F.3d 1165, 1171 (10th Cir.*5942002) (quoting Duvall v. Reynolds, 139 F.3d 768, 787 (10th Cir.1998)).
In rejecting his claim on direct appeal, the Oklahoma Court of Criminal Appeals (OCCA) found that:
Appellant had ample notice of the details of the proffered evidence and argued against its admissibility in a pretrial hearing; the trial court found a visible connection between the past conduct and the present offenses, given the age, gender, and other circumstances of the alleged victims. The trial court also instructed the jury on the limited use of the other-crimes evidence.
R., Vol. I, Doc. 1-1 at 2; Villareal v. State, No. F-2009-328, slip op. at 2 (Okla.Crim. App. Apr. 8, 2010). The district court agreed that E.J.’s testimony “demonstrated [Villarealj’s history as a sexual predator with young girls,” R., Vol. I, Doc. 15 at 4; Villarreal v. Patton, No. CIV-11-123RAW-KEW, 2014 WL 4966175, at *2 (E.D.Okla. Sept. 30, 2014), and further noted that this prior evidence of abuse demonstrated his lewd intent involved in his “pretend” tickling of another one of the victims, M.C., id.
In his application for a COA, Villareal has not presented any argument attacking the district court’s conclusion. Nor do we see any obvious flaws in the district court’s reasoning. Villareal’s prior acts provided probative evidence of his lewd intent in his-“pretend” tickling of M.C. Furthermore, E.J.’s age and family situation were similar enough to those of M.C. and J.Y. that E.J.’s testimony added credibility to their accounts. Whatever unfair prejudice may have resulted from E.J.’s testimony was mitigated by the trial court’s limiting instruction as well as by the fact that Villa-real was informed before trial of the state’s intent to call E.J. as a witness. Given this and Villareal’s lack of specific argument, we find that Villareal has not made a substantial showing that the OCCA’s resolution of this issue was contrary to clearly established Supreme Court precedent or that it was based on an unreasonable factual determination.
B. Double Jeopardy
Villareal next argues that the admission of evidence concerning M.O. violated the collateral estoppel component of the Constitution’s prohibition of double jeopardy because he had previously been acquitted of molestation charges relating to M.O. Villareal contends that because of his acquittal, collateral estoppel principles prohibited the state from asserting in his 2009 trial that he had molested M.O.
The Supreme Court has held that the doctrine of collateral estoppel is embodied in the Constitution’s Double Jeopardy Clause. Ashe v. Swenson, 397 U.S. 436, 445, 90 S.Ct. 1189, 25 L.Ed.2d 469 (1970). Collateral estoppel is the principle 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.” Id. at 443, 90 S.Ct. 1189. As the district court properly noted, however, the Supreme Court has already rejected the very argument Villareal now makes. In Dowling v. United States, the Court held that the collateral estoppel component of the Double Jeopardy Clause does not “exclude in all circumstances ... relevant and probative evidence that is otherwise admissible under the Rules of Evidence simply because it relates to alleged criminal conduct for which a defendant has been acquitted.” 493 U.S. 342, 348, 110 S.Ct. 668, 107 L.Ed.2d 708 (1990). As the court noted, an acquittal does not establish that a defendant is innocent of the charged crime; the most that an acquittal can establish is that there is reasonable doubt as to the defendant’s guilt. Id. at 348-50, 110 *595S.Ct. 668. Commission of a prior bad act, however, does not need to be proven beyond a reasonable doubt and evidence of such acts can be admitted, under the federal rules, “so long as a jury could reasonably conclude that the act occurred and the defendant was the actor.” Huddleston v. United States, 485 U.S. 681, 689, 108 S.Ct. 1496, 99 L.Ed.2d 771 (1988). Because of the lower standard for admitting such evidence, there is no necessary conflict between the first jury’s acquittal and the later admission of evidence concerning the earlier crime. Dowling, 493 U.S. at 348-50, 110 S.Ct. 668. The collateral estoppel component of the Double Jeopardy Clause thus does not prohibit the state from admitting evidence' of prior crimes, even where the defendant was acquitted. Id.
Again, Villareal has not presented any argument attacking the district court’s conclusion or explaining why this case is not governed by Dowling. As a result, we find that Villareal has not made a substantial showing that the OCCA’s resolution of this issue was contrary to clearly established Supreme Court precedent or that it was based on an unreasonable factual determination.
C. Ineffective Assistance of Counsel
Next, Villareal asserts that he was denied his Sixth Amendment right to effective assistance of trial counsel. More specifically, Villareal claims that his attorney should have objected to E.J.’s testimony concerning M.O. and the subsequent mentions of M.O. in closing arguments.
To prevail on a claim of ineffective assistance of counsel, a petitioner must prove both that counsel’s performance was deficient and that he was prejudiced as a result. Strickland v. Washington, 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Prejudice requires showing there is a “reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.” Id. at 694, 104 S.Ct. 2052. “A reasonable probability is a probability sufficient to undermine confidence in the outcome.” Id. This requires that “the likelihood of a different result. must be substantial, not just conceivable.” Harrington v. Richter, 562 U.S. 86, 112, 131 S.Ct. 770, 178 L.Ed.2d 624 (2011). Where a state court has already rejected an ineffective assistance claim, our review is limited to determining “whether the state court’s application of the Strickland standard was unreasonable.” Id. at 101, 131 S.Ct. 770.
Here, the OCCA considered and rejected Villareal’s ineffective assistance of counsel claim under Strickland’s prejudice prong:
[W]e find any such mistake to be harmless beyond a reasonable doubt. The testimony of the two complainants was positive and suffered from no obvious credibility issues, and the trial court •properly allowed other-crimes evidence from one witness. Any missteps on trial counsel’s part did not affect the outcome of the trial.
R., Vol. I, Doc. 1-1 at 2-3; Villareal, No. F-2009-328, slip op. at 2-3. Once again, Villareal has not developed or presented any argument contesting this finding, nor has our review of the record turned up anything that would allow us to deem this finding unreasonable. As a result, we must conclude that Villareal has not met his burden as to his third issue.
D. Cumulative Error
Finally, Villareal contends that the cumulative effect of the errors described above denied him his right to a fair trial. This argument, however, was not contained in his petition to the district court *596and thus has been waived. See Parker v. Scott, 394 F.3d 1302, 1327 (10th Cir.2005) (holding that issues not included in habeas petition have been waived); Jones v. Gibson, 206 F.3d 946, 958 (10th Cir.2000) (refusing to consider a cumulative error argument not raised in initial habeas petition). Given this, we decline to consider Villareal’s cumulative error argument.
III. Conclusion
For the reasons given above, Villareal’s application for a COA is DENIED and the appeal is DISMISSED.