
572 F.3d 1152 (2009)
UNITED STATES of America, Plaintiff-Appellee,
v.
Vojko RIZVANOVIC, Defendant-Appellant.
No. 08-4123.
United States Court of Appeals, Tenth Circuit.
July 17, 2009.
*1153 Bretta Pirie (Steven B. Killpack, Federal Public Defender, with her on the briefs), Utah Federal Defender's Office, Salt Lake City, UT, for Defendant-Appellant.
Stewart C. Walz, Assistant United States Attorney (Brett L. Tolman, United States Attorney, and Diana Hagen, Assistant United States Attorneys, with him on the brief), Salt Lake City, UT, for Plaintiff-Appellee.
Before BRISCOE, McKAY, and HARTZ, Circuit Judges.
McKAY, Circuit Judge.
Defendant Vojko Rizvanovic was charged with one count of international parental kidnapping, in violation of 18 U.S.C. § 1204(a), and two counts of making false statements in connection with a passport application, in violation of 18 U.S.C. § 1542. The case went to trial, where the jury found Defendant not guilty on both counts of making false statements but guilty on the kidnapping count. Defendant was sentenced to thirty-six months' imprisonment. On appeal, Defendant raises two issues. First, he argues that the district court erred by allowing the government to ask him on cross-examination about a state court's finding that he had abused his children and allowing the government to introduce rebuttal testimony from two witnesses that they each had witnessed him abuse the children. Second, he argues that the court erred by instructing the jury that the state court's finding was admitted not for the truth of the matter but for purposes of evaluating credibility and his testimony regarding the domestic violence.
The evidence introduced at trial established that Defendant had two young daughters, one born in 2002 and the second born in 2005, and that he and their mother had lived together from the late 1990s until the fall of 2006. In October 2006, the children's mother left the apartment in which she had been living with Defendant and took the children with her to a shelter. In subsequent custody proceedings, a state court judge found that Defendant had committed emotional and *1154 domestic abuse against the children and their mother, and the court awarded sole custody of the children to their mother. Defendant was permitted to have his first unsupervised visit with his daughters in December 2006. In February 2007, he was permitted his first overnight visit with his children, but he did not return them as scheduled. In March 2007, law enforcement officers learned that Defendant and the girls had been in Australia for the past three weeks and would soon be flying to Macedonia. Defendant was arrested on a layover in the Vienna airport, and the girls were returned to their mother.
At trial, Defendant conceded the elements of the kidnapping offense but asserted that his motivation fell within the statutory affirmative defense in 18 U.S.C. § 1204(c)(2), which applies when a parental kidnapper "was fleeing an incidence or pattern of domestic violence." Specifically, he testified that he had observed the children's mother abuse the children on several occasions when they were living together. He testified that her abuse became worse following her involuntary hospitalization for mental health reasons in the spring of 2005. He further testified that his main reason for taking the children was to protect them and prevent their mother from hurting them.
Following this testimony, the court overruled a defense objection and permitted the government to question Defendant about the state custody hearings and the state court's finding that Defendant had abused the children and their mother. In cross-examination, Defendant testified that four or five state custody hearings had occurred, that testimony was presented to the state judge at these hearings, and that he was represented by an attorney at the hearings. The government then asked whether the state judge found that he had committed emotional and domestic abuse against the children and their mother, and Defendant stated that he did not recall. The government then apparently showed Defendant the state court order. At this point, the court instructed the jury that this evidence was not admitted for the truth and should not be taken as proof of a factrather, the evidence was being presented simply for the jury to evaluate credibility and Defendant's testimony about the domestic violence. After this instruction was given, Defendant testified that the state court's finding was not true and that the reason the court did not find abuse by the children's mother was that he had not reported any.
The court also permitted the government to introduce rebuttal evidence from Defendant's seventeen-year-old stepdaughter, who testified there had been domestic violence in their home but Defendant was the sole perpetrator thereof. She testified that she had never seen her mother abuse the younger girls in any way but had seen Defendant hit one of them on numerous occasions. The government also introduced rebuttal evidence from the children's mother, who testified that she had never abused the children and that she had witnessed Defendant slap one of the girls.
"We review for abuse of discretion the extent to which a district court allows cross-examination of an accused." United States v. Crockett, 435 F.3d 1305, 1312 (10th Cir.2006). We also review a challenge to the admission of rebuttal testimony for abuse of discretion. United States v. Magallanez, 408 F.3d 672, 680 (10th Cir.2005). "Under that standard, we will not disturb an evidentiary ruling absent a distinct showing that it was based on a clearly erroneous finding of fact or an erroneous conclusion of law or manifests a clear error in judgment." United States v. Jenkins, 313 F.3d 549, 559 (10th Cir.2002).
*1155 Defendant argues that the evidence of his abuse was not relevant to the question whether the children's mother was abusive and should not have been admitted on cross-examination or in rebuttal. He argues that there is not a limit of one abuser per family and thus his alleged abuse had no bearing on his affirmative defense that he was fleeing a pattern or incident of domestic violence against the children. However, in light of Defendant's testimony that his main reason for taking the children and leaving the country was "to protect the children" (Vol. 3a at 19), we conclude that the district court did not abuse its discretion by allowing the government to introduce the contested evidence. Evidence related to Defendant's domestic violence was relevant to the jury's assessment of Defendant's testimony regarding his motivationin light of this evidence, the jury might reasonably doubt that Defendant was actually motivated by a desire to protect his children from harm or abuse. And, Defendant's admission that he never reported any abuse by the children's mother in four or five state custody hearings at which he was represented by an attorney could properly be considered by the jury in its assessment of the credibility of Defendant's current testimony that their mother had regularly and repeatedly abused the children for at least seventeen months prior to the time she left Defendant. We agree with the district court that this evidence was relevant, and we are not persuaded that this evidence was so prejudicial that its admission constituted an abuse of discretion by the district court.[1] We therefore affirm the district court's admission of this evidence.
Defendant's second argument on appeal is that the district court erred in instructing the jury that the state court's finding of abuse was admitted not for the truth but only for purposes of assessing credibility. Defendant did not object to this instruction either when the judge proposed it at a bench conference or when the judge actually gave it to the jury.[2] We therefore review this issue only for plain error. "Plain error occurs when there is (1) error, (2) that is plain, which (3) affects substantial rights, and which (4) seriously affects the fairness, integrity, or public reputation of judicial proceedings." United States v. Gonzalez-Huerta, 403 F.3d 727, 732 (10th Cir.2005) (en banc) (internal quotation marks omitted).
*1156 When the government questioned Defendant regarding the state court order, the court gave the following instruction to the jury:
Let me first tell you the purpose of this testimony. When I was first giving you instructions, I told you sometimes you might hear something for a limited purpose. This is one of those times. What you are hearing and what the state court judge ... found is not offered for the truth, nor should you take it as a proof of a fact. It's being heard by you simply for you to evaluate first of all credibility and then, secondly, to evaluate the testimony you have heard from Mr. Rizvanovic about the domestic violence, but it is not for the truth.
(Vol. 3a at 56-57.) Defendant does not argue that a different limiting instruction would have been more appropriate. Rather, he simply argues that the admission of the contested evidence was rendered more prejudicial by the court's giving of this instruction, which improperly suggested that the jury should use the state court's finding of abuse to assess his credibility without regard to whether that finding was true.
Assuming that this instruction would meet the first two prongs of the plain error test, we conclude that Defendant has not satisfied the third prong of the test because he has not shown how this instruction prejudiced his substantial rights. It is difficult to see how the alternativethe bald admission of evidence that a state court had found Defendant to be abusive would be less prejudicial than the admission of this evidence with an instruction that the court's finding should not be considered to be proof of a fact and should be considered only in weighing Defendant's credibility. Defendant cites to no case in which a court has found more prejudice from the admission of evidence with a limiting instruction than without, and we conclude that such a counterintuitive situation does not exist in this case. Although the instruction may have been somewhat confusing, we conclude that any error in the instruction inured to Defendant's benefit because it tended to give less weight to the state court's finding of abuse, rather than more.
For the foregoing reasons, we reject both of the challenges Defendant raises on appeal. His conviction and sentenced are AFFIRMED.
NOTES
[1]  Rule 608(b) of the Federal Rules of Evidence prohibits proving specific instances of conduct by extrinsic evidence for impeachment purposes. In this case, the government cross-examined Defendant as to whether he had abused his children and their mother, and the court allowed rebuttal evidence tending to disprove his answers. Rule 608(b) does not bar extrinsic evidence to the extent it goes to substantive issues, and here the rebuttal evidence tended to disprove Defendant's affirmative defense that he took the children to free them from domestic violence.
[2]  Defendant suggests on appeal that defense counsel would have objected to the instruction if the court had not interrupted his objection to the admission of this evidence on relevancy grounds. However, we see no indication in the record that Defendant intended to or was prevented from raising an objection to the proposed instruction. Before launching into his relevancy argument, counsel indicated that this was the last point he wanted to make. Moreover, while the court did stop defense counsel from repeating the relevancy argument, counsel had several later opportunities to discuss the admission of the evidence and the proposed instruction with the court, and at no point did counsel even hint that the instruction might be problematic. Furthermore, even if we were to review this issue de novo as Defendant suggests, we would find any error in the instruction harmless because, as discussed above, we conclude that any error in the instruction inured to Defendant's benefit.
