Petitioners Miguel Antonio Rodriguez Rodriguez and Adriana Patricia Valbuena Arias, and their children, Miguel Angel Rodriguez Valbuena and Juanita Rodriguez Valbuena, seek review of the Board of Immigration Appeals’ (“BIA”) decision affirming the Immigration Judge’s (“IJ”) order denying their application for asylum, withholding of removal under the Immigration and Nationality Act (“INA”), and relief under the Convention Against Torture (“CAT”). On appeal, they argue that: (1) substantial evidence did not support the IJ’s adverse credibility determination, and, moreover, that the determination violated then* right to due process; and (2) on the merits, the IJ’s denial of asylum was erroneous. After thorough review, we dismiss the petition in part, and deny it in part.
We review jurisdictional questions de novo. Amaya-Artunduaga v. U.S. Att’y Gen., 463 F.3d 1247, 1250 (11th Cir.2006). When evaluating a petition for review of an order by the BIA denying an application for asylum and withholding of removal, we review findings of fact under the highly deferential substantial evidence test, and must affirm the decision if it is “supported by reasonable, substantial, and probative evidence on the record considered as a whole.” Forgue v. U.S. Att’y Gen., 401 F.3d 1282, 1286 (11th Cir.2005) (quotation omitted). Moreover, we review the record evidence in the light most favorable to the agency’s decision, and may not overturn findings of fact unless the record compels it. Id. at 1286-87. Because credibility determinations constitute factual findings, we review such determinations under the substantial evidence test, and will not substitute our judgment for that of the IJ or BIA. Id. at 1286.
When the BIA issues a separate decision, we review only that decision, “except to the extent that [the BIA] expressly adopts the IJ’s opinion.” Al Najjar v. Ashcroft, 257 F.3d 1262, 1284 (11th Cir.2001). “Insofar as the [BIA] adopts the IJ’s reasoning, we will review the IJ’s decision as well.” Id. We, however, will not review the IJ’s decision as to an issue not addressed by the BIA. Instead, if necessary, we must remand the case to give the BIA “the opportunity to address the matter in the first instance in light of its own expertise.” INS v. Ventura, 537 U.S. 12, 16-17, 123 S.Ct. 353, 154 L.Ed.2d 272 (2002).
As an initial matter, we lack jurisdiction over the petitioners’ due process claim and over their claim that the IJ erred when he found that Rodriguez was not a victim of past persecution on account of political opinion. We may not review a final order of removal unless “the alien has exhausted all administrative remedies available to the alien as of right.” 8 U.S.C. § 1252(d)(1). If a petitioner fails to exhaust available administrative remedies, we lack jurisdiction to consider the claim. Amaya-Artunduaga, 463 F.3d at 1250. In Amaya-Artunduaga, we held that an alien did not exhaust administrative remedies when he failed to raise his due process claim before the BIA. Id. at 1251.
*374In this case, we do not have jurisdiction to review the petitioners’ due process claim because they failed to exhaust administrative remedies by not raising that claim in their notice of appeal or brief to the BIA. See 8 U.S.C. § 1252(d)(1); Amaya-Artunduaga, 463 F.3d at 1250-51. We also cannot review their claim that the IJ erred by denying them asylum on the merits, because the BIA did not reach that issue, but simply affirmed the IJ’s adverse credibility determination and reasoned from there. See Ventura, 537 U.S. at 16-17, 123 S.Ct. 353. We therefore dismiss the petition as to these two claims.
We also reject the petitioners’ argument that substantial evidence did not support the IJ’s adverse credibility determination. An alien who arrives in or is present in the United States may apply for asylum. 8 U.S.C. § 1158(a)(1). The Attorney General has discretion to grant asylum if the alien meets the INA’s definition of a “refugee.” 8 U.S.C. § 1158(b)(1)(A). A “refugee” is:
any person who is outside any country of such person’s nationality or, in the case of a person having no nationality, is outside any country in which such person last habitually resided, and who is unable or unwilling to return to, and is unable or unwilling to avail himself or herself of the protection of, that country because of persecution or a well-founded fear of persecution on account of race, religion, nationality, membership in a particular social group, or political opinion.
8 U.S.C. § 1101(a)(42)(A). The asylum applicant carries the burden of proving statutory “refugee” status. Al Najjar, 257 F.3d at 1284. To establish asylum eligibility, the alien must, with specific and credible evidence, establish (1) past persecution on account of political opinion or any other protected ground, or (2) a well-founded fear that political opinion or any other protected ground will cause future persecution. 8 C.F.R. § 208.13(a) and (b). To qualify for withholding of removal, an applicant must establish that it is more likely than not that the applicant’s “life or freedom would be threatened on account of race, religion, nationality, membership in a particular social group, or political opinion.” Mendoza v. U.S. Att’y Gen., 327 F.3d 1283, 1287 (11th Cir.2003) (citing 8 U.S.C. § 1231(b)(3)(A)). When a petitioner fails to establish a claim of asylum on the merits, that petitioner “necessarily fails to establish eligibility for withholding of removal.” Forgue, 401 F.3d at 1288 n. 4. This is because the standard for withholding of removal is significantly higher than the asylum standard. See Amaya-Artunduaga, 463 F.3d at 1249 n. 3. If an IJ makes a finding that a petitioner is not entitled to asylum, that IJ is “not obligated to make specific findings with respect to withholding of removal.” Id.
An applicant’s testimony, if credible, may carry that applicant’s burden of proof without corroboration. 8 C.F.R. § 208.13(a). “Conversely, an adverse credibility determination alone may be sufficient to support the denial of an asylum application.” Forgue, 401 F.3d at 1287. Nevertheless, if an applicant who is not a credible witness produces other evidence of persecution aside from his testimony, the IJ and BIA must consider that evidence. Id. “The weaker an applicant’s testimony, however, the greater the need for corroborative evidence.” Yang v. U.S. Att’y Gen., 418 F.3d 1198, 1201 (11th Cir.2005).
In order to enable our review of credibility findings, the IJ must make a clean, explicit determination of credibility. Id. “Once an adverse credibility finding is made, the burden is on the applicant alien to show that the IJ’s [and BIA’s] credibility decision was not supported by specific, cogent reasons or was not based on substantial evidence.” Forgue, 401 F.3d at *3751287 (quotation omitted). “Indications of reliable testimony include consistency on direct examination, consistency with the written application, and the absence of embellishments.” Ruiz v. U.S. Att’y Gen., 440 F.3d 1247, 1255 (11th Cir.2006).
The Real ID Act of 2005 (“RIDA”), which amended the INA’s asylum provisions, provides:
Considering the totality of the circumstances, and all relevant factors, a trier of fact may base a credibility determination on the demeanor, candor, or responsiveness of the applicant or witness, the inherent plausibility of the applicant’s or witness’s account, the consistency between the applicant’s or witness’s written and oral statements (whenever made and whether or not under oath, and considering the circumstances under which the statements were made), the internal inconsistency of each such statement, the consistency of such statements with other evidence of record (including the reports of the Department of State on country conditions), and any inaccuracies or falsehoods in such statements, without regard to whether an inconsistency, inaccuracy, or falsehood goes to the heart of the applicant’s claim, or any other relevant factor.
Pub.L. No. 109-13, § 101(a)(3), (d)(2), 119 Stat. 231, 303, 304-05 (codified at 8 U.S.C. §§ 1158(b)(l)(B)(iii), 1229a(c)(4)(C)). This provision of RIDA applies to asylum applications filed after May 11, 2005. Pub.L. No. 109-13, § 101(h)(2), 119 Stat. at 305.
In this case, the IJ made a clean adverse credibility determination against Rodriguez. The IJ explicitly found Rodriguez’s testimony inconsistent and not credible. See Yang, 418 F.3d at 1201. Moreover, substantial evidence supported that determination. The IJ noted, and Rodriguez now admits, that Rodriguez’s wife’s testimony contradicted Rodriguez’s testimony regarding at what time and to whose house in Bogotá Rodriguez returned after the roadblock shooting incident. While the discrepancy regarding the time is relatively minor, the discrepancy regarding at whose house Rodriguez and his wife were staying at the time is stark. Under RIDA, which applies to this case, the IJ was free to base his credibility determination on this inconsistency of Rodriguez’s testimony “with other evidence of record,” such as his wife’s testimony. 8 U.S.C. §§ 1158(b)(l)(B)(iii).
In addition, the BIA also considered Rodriguez’s nontestimonial evidence. See Forgue, 401 F.3d at 1287. The BIA expressly explained how Rodriguez’s submitted documents, including photographs of the car, a newspaper article, and Sermiento’s death certificate, failed to corroborate his testimony. And since Rodriguez’s testimony contradicted his wife’s testimony on two grounds, the need for corroborative evidence was all the greater. See Yang, 418 F.3d at 1201.
Finally, because the IJ did make a clean credibility finding, it is Rodriguez’s burden to show that the finding was not supported by specific, cogent reasons, or was not based on substantial evidence. See Forgue, 401 F.3d at 1287. Rodriguez, however, cannot bear that burden here because all of his arguments are without merit. First, because RIDA applies to the case, the IJ was free to base his credibility finding on inconsistencies that did not go the heart of Rodriguez’s claim. See 8 U.S.C. §§ 1158(b)(l)(B)(iii). Second, while Rodriguez in his brief argues that “relevant and persuasive evidence” explained the alleged discrepancies, he does not, and cannot, point to any such evidence. Third, the discrepancies were not due to his wife’s lack of personal knowledge of the details of the incidents. The discrepancies concerned facts squarely within her personal knowledge, namely, where she was staying on December 20, 2005, and at what *376time Rodriguez returned there that night. Moreover, her testimony does not indicate that it was based on anything other than her personal knowledge of those facts. Fourth, even if Rodriguez’s own testimony closely mirrored his application addendum statement, that consistency did not negate the inconsistencies between his and his wife’s testimony. And lastly, given that Rodriguez bore the burden of establishing that he was entitled to relief, it was not the IJ’s duty to bring the discrepancies to the attention of the witnesses. See Al Najjar, 257 F.3d at 1284. These were not mere ambiguities that reasonably called for clarification on the record.
Because Rodriguez cannot establish that the adverse credibility finding was not based on substantial evidence, and given that such a finding is sufficient to support the denial of asylum, and, necessarily, withholding of removal, we deny the petition regarding this claim. See Forgue, 401 F.3d at 1287,1288 n. 4.
PETITION DISMISSED IN PART, DENIED IN PART.