ORDER
Ah Bazzi and Amina Bazzi have petitioned for judicial review of an order of the Board of Immigration Appeals (“BIA”), which affirmed an immigration judge’s finding that they were subject to removal. The parties have waived oral argument, and the panel unanimously agrees that it is not needed in this ease. Fed. R.App. P. 34(a).
The Bazzis are natives of Lebanon, who entered the United States as visitors for pleasure in 1989 and 1990. The Immigration and Naturalization Service initiated removal proceedings against them in 1998, alleging that they had remained in this country beyond the time that was authorized by their visas. The Bazzis conceded deportability and applied for asylum and the withholding of deportation. They also requested protection under the United Nations Convention Against Torture and the privilege of voluntary departure.
An immigration judge (“IJ”) conducted a final hearing on June 1, 2001, at which the *885Bazzis were represented by counsel. Amina Bazzi did not testify, but Ali Bazzi testified that he had been persecuted by the opposing political factions of Hezbollah and the South Lebanese Army (“SLA”) because he had refused to cooperate with either group. The IJ found that this testimony was not fully credible and denied the Bazzis’ applications for asylum and the withholding of removal. He also denied their request for voluntary departure and their petition for relief under the Convention Against Torture. This opinion became the final decision of the agency on October 4, 2002, when the BIA dismissed the Bazzis’ administrative appeal.
Initially, we note that the Bazzis have not raised any clear challenge to the denial of their application for relief under the Convention Against Torture. Hence, they have waived this claim for purposes of judicial review. See United States v. Mick, 263 F.3d 553, 567 (6th Cir.2001).
An asylum application is also treated as an application for the withholding of removal, even though the burden of proving eligibility for asylum is less onerous. Mikhailevitch v. INS, 146 F.3d 384, 391 (6th Cir.1998). To obtain asylum, he Bazzis must show that they are refugees and that their applications merit a favorable exercise of administrative discretion. See id. at 389. The IJ did not reach the discretionary step here, as the Bazzis did not meet their burden of proving that they are refugees. A refugee is defined as “an alien who is unable or unwilling to return to his home 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.” Id. (citations and internal quotation marks omitted) (quoting INS v. Elias-Zacarias, 502 U.S. 478, 481, 112 S.Ct. 812, 117 L.Ed.2d 38 (1992)).
A petition for judicial review may be granted only if the evidence is so compelling that no reasonable fact-finder could fail to find the requisite fear of persecution. Koliada v. INS, 259 F.3d 482, 486 (6th Cir.2001). Thus, the BIA’s decision must be upheld if it is supported by reasonable, substantial, and probative evidence, even if we might have decided the case differently. See id.
Ali Bazzi alleged that he had been detained and mistreated by the SLA when they tried to recruit him in 1989, and that he had been aggressively recruited by the Hezbollah in 1990. Thus, the Bazzis alleged that they feared persecution in Lebanon because Ali Bazzi had refused to join the Hezbollah and because the Hezbollah might believe that he had worked for the SLA. Amina Bazzi did not testify, but she apparently asserts that she will be persecuted because of her relationship to her husband and because she traveled through Israel when she came to the United States.
The IJ found that Ali Bazzi was not fully credible, citing several inconsistencies between his asylum application and hearing testimony that were central to the merits of his claims. Bazzi testified that he did not know who killed his father or why he was killed, even though his asylum application had indicated that his father was killed by the Hezbollah. Bazzi’s testimony also indicates that he was not kicked, punched or beaten with a rubber hose by the SLA, even though he had alleged as much in his application. Moreover, Bazzi gave varied and inconsistent testimony regarding the timing and the number of times that he was allegedly detained by the SLA.
The Bazzis now argue that the IJ erred by relying on a lack of corroborating evidence. However, the IJ properly noted the absence of corroborative evidence only after the inconsistencies in Bazzi’s testimony had placed his credibility in doubt. See Chebchoub v. INS, 257 F.3d 1038, 1043-45 (9th Cir.2001). Thus, we conclude that *886substantial evidence supports the IJ’s credibility finding. See id. In light of this finding, the Bazzis have failed to present compelling evidence in support of their claims. See Elias-Zacarias, 502 U.S. at 483-84, 112 S.Ct. 812; Chebchoub, 257 F.3d at 1045.
The IJ also found that they would not have had a persuasive claim even if Ali Bazzi’s testimony had been credible. In this regard, we note that Bazzi did not show that he had been seriously mistreated by the Hezbollah and that he has not had contact with either group in fourteen years. Moreover, Bazzi testified that the SLA member who had allegedly persecuted him is now dead and a State Department Country Report indicates that the SLA no longer exists.
The evidence in this case does not compel a finding that the Bazzis are refugees, as it does not indicate that they have a well-founded fear of persecution. See Koliada, 259 F.3d at 487-88; Chebchoub, 257 F.3d at 1045. Since substantial evidence supports the IJ’s finding that they are not refugees, we need not reach the question of whether their asylum applications merit a favorable exercise of discretion. See Koliada, 259 F.3d at 488. As the Bazzis have not established eligibility for asylum, they are necessarily unable to meet the more rigorous standard required for the withholding of removal. See id. at 489; Mikhailevitch, 146 F.3d at 391.
Finally, the Bazzis argue that the IJ should have granted their request for voluntary departure. However, that issue is not cognizable in an action for judicial review. 8 U.S.C. § 1252(2)(B).
Accordingly, the Bazzis’ petition for judicial review of the BIA’s decision is denied.