POOLER, Circuit Judge.

Elida Karaj ("Elida"), her husband, Avdyl Karaj ("Avdyl"), and their two minor sons, Abli and Amir, petition for review of an order of the Board of Immigration Appeals ("BIA") that summarily affirmed an immigration judge's ("IJ") order directing the Karajs' removal and denying their requests for asylum pursuant to 8 U.S.C. § 1158(b)(1), withholding of removal pursuant to 8 U.S.C. § 1231(b)(3)(A), and relief under the United Nations Convention Against Torture and Other Cruel, Inhuman or Degrading Treatment or Punishment ("CAT"), adopted by UN Gen. Assembly December 10, 1984, S. Treaty Doc. No. 100-20 (1988), 1465 U.N.T. S. 85. We dismiss petitioners' withholding-of-removal and CAT claims because petitioners failed to exhaust their administrative remedies. However, we hold that the Karajs did exhaust their administrative remedies with respect to their asylum claim, and we remand for further findings based on lack of clarity in the IJ's decision concerning the reasons why he denied the Karajs relief and a significant error in his statement of the standard the Karajs must satisfy to be entitled to asylum.

BACKGROUND

The Karajs, natives and citizens of Albania, claim past persecution based on Elida's membership in the Albanian Democratic party. They describe maltreatment of Elida and her family of origin by the former Communist regime and complain that the Socialists, after coming to power in 1996, also continually harassed Elida. In addition, Elida and Avdyl testified to three specific incidents of alleged persecution.

First, in December 1998, Avdyl was arrested during an anniversary celebration/demonstration for the Democratic party. He was kept for two or three hours, hit with a rubber club, and threatened with more severe treatment. Avdyl was also warned that it would be his wife's turn next. Second, on November 8, 1999, a bomb exploded in front of the Karajs' residence. The next day Elida went to the police station to report the occurrence. Instead of acting on her complaint, the police handcuffed her and put her in a cell. She recognized one of the policemen as a member of the Socialist party who "was always revenging against [her]." Elida was kept and threatened until she withdrew her complaint. During her detention, the officers "started grabbing [her] and laughing." Third, on May 5, 2000, Elida saw a van with police markings in front of a store. Three persons in civilian dress emerged from the van and tried to grab her. Two neighbors then came out and started fighting with Elida's attackers, who hit Elida with their fists. The attackers fled when one of the neighbors threatened them with a gun.

In his decision on the Karaj s' application, IJ George T. Chew found it unnecessary to articulate the substantive law governing asylum, withholding of removal, and CAT relief because that law "is very well established." He held that "the respondents have] not met their burden of showing that they would be persecuted upon their return." He based this holding "largely on the implausibility of the respondent's story and her testimony." He noted specifically that Elida could not explain in her testimony why the Socialists would select her and her husband for persecution when she was only a member of the Democratic party, and Avdyl admittedly was not even a member of the party but only a sympathizer. In addition, because the IJ found that Elida was unable to articulate answers to simple questions on cross examination, he believed she had "memorized much of her testimony." Further, the IJ pointed out that Elida's documents were issued after she came to the United States and that a letter from the Democratic Party did not indicate when she joined the party. The IJ also cited the Country Report for the proposition that "Albania is a country in great flux." Finally, IJ Chew was "troubled by the fact that the respondent's conveniently lost all of the passports that they entered this country with" and that Avdyl had no identification documents.

The IJ ended his decision by saying: "In total the Court, in weighing the respondent's testimony, will conclude that she has not satisfied her burden and accordingly, will deny her application for asylum. Having denied her application for asylum, the Court will also deny her applications for withholding of removal and relief under the Convention Against Torture."

On appeal to the BIA, the Karajs asked in the prayer for relief in their brief for reversal of the IJ's determinations on asylum and withholding of removal but did not mention CAT relief. As to asylum, the Karajs said: "the United States Supreme Court [has] held that[,] in an application for asylum[,] a well-founded fear of persecution equals a less than fifty percent probability of persecution and that a small probability may suffice" and argued that they had met that standard. Pets.' BIA Mem. at 2 (citing INS v. Cardoza-Fonseca, 480 U.S. 421, 107 S.Ct. 1207, 94 L.Ed.2d 434 (1987)). Although petitioners also set forth the facts supporting their asylum application, they did not explicitly argue that the IJ applied an incorrect standard to that claim. Petitioners made no argument relevant to their withholding of removal or CAT claims and relied on no language from any case that might be construed as identifying an error on the IJ's part in denying these claims. The BIA affirmed without opinion.

On appeal, the Karajs contend that the IJ (1) applied a standard that was too rigorous when he denied their asylum claim; (2) erred by failing to determine whether Elida had suffered past persecution; and (3) used the wrong standard in evaluating the Karajs' withholding-of-removal and CAT claims. In addition to defending the IJ's decision on the merits, respondent contends that the Karajs are barred from raising the standard-of-review issues because they did not raise them before the BIA.

DISCUSSION

I. Standard of Review

We briefly summarize the well known principles applicable to our review. First, because the BIA summarily affirmed the IJ's decision, we review the IJ's decision directly. Zhi Wei Pang v. Bureau of Citizenship and Immigration Services, 448 F.3d 102, 107 (2d Cir. 2006). Second, we confine our review to the reasons given by the IJ and will not search the record for alternative reasons to affirm. Secaida-Rosales v. INS, 331 F.3d 297, 305 (2d Cir. 2003). Third, where the IJ makes factual findings, including credibility findings, we apply a substantial evidence standard of review. See Zhou Yun Zhang v. INS, 386 F.3d 66, 73 (2d Cir. 2004); see also 8 U.S.C. § 1252(b)(4)(B). In fact, the IJ's opportunity to judge demeanor causes us to grant "particular deference" to credibility findings based on demeanor. See Zhou Yun Zhang, 386 F.3d at 73. Finally, where the IJ makes an error of law, we normally will vacate his or her decision. See Jin Shui Qiu v. Ashcroft, 329 F.3d 140, 149 (2d Cir. 2003).

II. Asylum

"To establish eligibility for asylum, a petitioner must show that . . . he has suffered past persecution on account of `race, religion, nationality, membership in a particular social group, or political opinion,' or that he has a well-founded fear of future persecution on these grounds." Id. at 148 (quoting 8 U.S.C. § 1101(a)(42)). Proof of past persecution creates a rebuttable presumption of a well-founded fear of future persecution. Id. Further, at least since 1987, it has been clear that an asylum applicant need not show that she "probably" will be persecuted if returned to her country of origin. See Cardoza Fonseca, 480 U.S. at 440, 107 S.Ct. 1207. Rather, as little as a 10% probability of persecution may suffice. See id. The Karajs' primary argument on appeal is that the IJ did not apply the Cardoza Fonseca standard but instead (1) required them to prove that they "would be persecuted" on return, and (2) failed to evaluate their evidence of past persecution.

Respondent argues that the Karajs' asylum claim must be dismissed insofar as it relies on the IJ's imposition of an erroneously heightened burden because the Karaj s failed to exhaust administrative remedies by alerting the BIA to the IJ's claimed error. The Karajs, however, contend that they sufficiently exhausted this argument by citing Cardoza-Fonseca and articulating the correct standard as the basis for their appeal.

Congress has limited this court's power to review a final order of removal to those removal orders for which "the alien has exhausted all administrative remedies available to the alien as of right." 8 U.S.C. § 1252(d)(1). This provision is jurisdictional. See Foster v. INS, 376 F.3d 75, 77 (2d Cir. 2004). However, we continue to refine our view of the specificity with which issues and arguments must be raised to the IJ and BIA. Compare Drozd v. INS, 155 F.3d 81, 85, 90-91 (2d Cir. 1998) (holding that an argument that petitioner should be granted United States citizenship was waived by petitioner's failure to raise it to the BIA, although petitioner had argued that he was already a citizen) with Johnson v. Ashcroft, 378 F.3d 164, 170 n. 7 (2d Cir. 2004) (holding that if a petitioner makes the substance of his argument known to the BIA, his failure to cite precise regulations and precedents is not fatal); see also Gill v. INS, 420 F.3d 82, 86 (2d Cir. 2005) (stating that while petitioner may not "rais[e] a whole new category of relief on appeal" and "must have raised an issue below to raise it on appeal," "we have never held that a petitioner is limited to the exact contours of his argument below").

We believe that the Karajs sufficiently exhausted their standard-of-review argument on the asylum claim. Because Cardoza-Fonseca delineates the difference between the standard for granting asylum (a well-founded fear of persecution) and the standard for granting withholding of removal (clear probability of persecution) and holds that it is wrong to require an asylum applicant to meet the standard for withholding of removal, see 480 U.S. at 423-24, 448, 107 S.Ct. 1207, and the Karajs' brief to the BIA articulated the correct asylum standard, the BIA was adequately presented with the Karajs' contention that it should review the facts pursuant to the well founded fear standard rather than requiring them to show they would be persecuted upon return to Albania. Although petitioners did not explicitly argue that the IJ placed an incorrectly heightened burden on them, their statement of the correct standard and citation of Cardoza-Fonseca, was enough to alert the BIA to the IJ's error. Cf Johnson, 378 F.3d at 170 n. 7. Where, as here, it is clear from the face of the IJ's decision that he used the wrong standard, and petitioner cited and urged in argument to the BIA the use of the correct standard, the petitioner has sufficiently exhausted his or her administrative remedies on a claim that the IJ employed the wrong standard. Cf. id.

Our conclusion is buttressed by a decision in the somewhat analogous context of a state habeas petitioner's exhaustion of federal constitutional claims. A state prisoner may exhaust his federal constitutional claim before a state appellate court by, inter aha, relying on federal constitutional cases or even on state cases that cite federal constitutional cases. See Daye v. Attorney Gen., 696 F.2d 186, 194 (2d Cir. 1982) (in banc). In like manner, the Karajs sufficiently exhausted their claim that the IJ erroneously imposed a heightened burden on them for proving entitlement to asylum by stating the correct standard and citing the case establishing it.

The IJ's own words — "the respondents have] not met their burden of showing that they would be persecuted upon their return" — demonstrate that he imposed an improperly heightened burden on the Karajs. Respondent's contention that, despite some inartful language, the IJ actually judged the Karajs' proof under the correct standard, is not persuasive. In Guan Shan Liao v. DOJ, 293 F.3d 61 (2d Cir. 2002), on which respondent relies, we reviewed a BIA opinion that stated, in part:

We find that the applicant has not established that he falls within the new definition of refugee on the basis of his having been fined because his son applied for a marriage license while underage and for harboring his cousin who had fled from birth control officials believing that he might be sterilized, having his house sealed after the family had left, and having been ordered to report for a study class on birth control policies. The applicant has not shown that these actions constitute "such resistance" to the government's family planning policies that he would be subject to persecution upon his return to China.

Id. at 68. Later in its opinion, the BIA said:

We find that the evidence of record, considered cumulatively, does not show that the applicant has met his burden of demonstrating that he has suffered past persecution or has a well-founded fear of persecution on account of one of the five grounds for which asylum may be granted.

Id. at 74 (Jacobs, J., concurring and adding emphases).

The Guan Shan Liao majority found that the first quoted paragraph could be read to incorrectly suggest that an applicant for asylum must show that he would face persecution if returned to his country of origin. Id. at 68-69. The court concluded, however, that the "two sentences [should be read] as simply faulting the applicant for failing to show that any of these actions would even potentially subject Liao to persecution upon his return to China." Id. at 69. Judge Jacobs, writing in concurrence, focused on the second quoted paragraph, arguing that it eliminated any potential ambiguity by clearly stating the correct standard. Id. at 74.

Unlike the BIA opinion addressed in Guan Shan Liao, the IJ opinion in this case contains no ambiguity and no language suggesting that the IJ actually applied or even knew the correct standard for asylum. The IJ's only comment on what the Karajs would be required to prove was: "The respondents have] not met their burden of showing they would be persecuted upon their return." Because this statement is not ambiguous and is the only statement of a standard in the IJ's decision, it must be accepted at face value.

Respondent also contends that we should ignore the error in the IJ's statement of the burden because the IJ explained that his finding that Elida did not meet her burden was "base[d] largely on the implausibility of the respondent's story and her testimony." We assume that this argument is based on the premise that the IJ made a credibility finding that would have applied regardless of the showing required for relief. The argument is not persuasive. The IJ made a significant error in applying the wrong standard to Elida's asylum claim. On the record before us, it is impossible to know how this error affected the IJ's overall conclusion, particularly given the IJ's ambiguous and confusing reasoning in which he blended together factors that relate to credibility with factors that do not. In short, the IJ's reasoning, viewed in the light of his application of a heightened standard, is too obscure to permit meaningful judicial review. See Secaida-Rosales, 331 F.3d at 305-06. We therefore cannot confidently predict what the IJ would do on remand. See Xiao Ji Chen v. U.S. Dep't of Justice, 434 F.3d 144, 158 (2d Cir. 2006) (stating that we may affirm a decision of the BIA where we can confidently predict that, absent any errors we have identified, the IJ would reach the same decision on remand).

Finally, respondent argues that the incidents to which the Karajs testified are not persecution as a matter of law. We, however, must review the findings the IJ actually made and not seek out bases for denying review on which the IJ did not rely. See Zhi Wei Pang, 448 F.3d at 107. The IJ did not find that, even crediting the Karajs' testimony, they had not established past persecution or a well-founded fear of future persecution. Instead the IJ found that the Karaj s had not established that they would face persecution if returned to Albania. Because the IJ did not determine whether petitioners met the appropriate standard and did not clearly determine that petitioners' testimony lacked credibility, we must remand for appropriate findings on both issues.

III. Withholding of removal and CAT relief

Although the Karajs asked in their prayer for relief that the BIA reverse the IJ's denial of withholding of removal, they made no argument relevant to this claim. Further, the Karaj s did not seek reversal of the IJ's denial of their CAT claim. The failure to seek review of the CAT claim deprives us of jurisdiction. See Beharry v. Ashcroft, 329 F.3d 51, 59 (2d Cir. 2003) (holding that, assuming statutory exhaustion requirement applied to asylum claims raised in a habeas petition, court lacked jurisdiction to consider alien's entitlement to a form of relief that he did not request in administrative proceedings). Although the Karajs asked the BIA to reverse the IJ's denial of withholding of removal in their prayer for relief, the Karajs' failure to make any argument to the BIA in support of their withholding-of-removal claim or to identify, even by implication, any error in the IJ's ruling on this claim, similarly bars our consideration of that claim. See Foster, 376 F.3d at 78 (holding that making a generalized argument that petitioner was not subject to removal did not exhaust argument that the crime for which petitioner had been convicted was not an aggravated felony justifying removal).

Notwithstanding these clear principles, petitioners contend that they sufficiently exhausted their withholding-of-removal and CAT claims because the single BIA member who determines whether an IJ's decision is appropriate for the board's streamlined procedure must first determine that the IJ reached the correct result. See 8 C.F.R. § 1003.1(e)(4). In order to determine correctness, the Karajs urge, the BIA was required to identify and apply the correct burden for proving entitlement to withholding of removal and CAT relief.

The Ninth Circuit has considered the applicability of the exhaustion requirement in the context of the streamlined procedure allowed by Section 1003.1(e)(4). See Zara v. Ashcroft, 383 F.3d 927 (9th Cir. 2004). The Zara court rejected an argument similar to the Karajs' argument because, in part, "[t]he policy underlying the exhaustion requirement is to give an administrative agency the opportunity to resolve a controversy or correct its own errors before judicial intervention." Id. at 931. The Zara court further reasoned:

When deciding whether to streamline a case, the BIA evaluates, among other things, whether the issues on appeal are squarely controlled by existing precedent or are so insubstantial that three-member review is not warranted. Accordingly, the decision whether to streamline is affected by what issues the petitioner chooses to appeal to the BIA. The failure to include issues may result in a decision to streamline which otherwise would not have been made. . . . If we were to hold that the BIA's streamlining decision excused the administrative requirement of exhaustion of remedies, we would legitimize the very vice the exhaustion requirement was designed to prevent, namely premature interference with the agency's processes.

Id. (internal quotation marks and citation omitted).

Judge Tashima, writing in dissent, disagreed. He argued, as petitioners do, that because the BIA must insure that the "result " reached by the IJ was correct and that "any errors in the decision under review were harmless or non material," the BIA must consider all issues raised by the decision whether or not the petitioner raises them. Id. at 933 (Tashima, J., dissenting) (quoting and adding emphases to former 8 C.F.R. § 3.1(a)(7)(ii), renumbered as 8 C.F.R § 1003.1(e)(4)(i)).

We respectfully disagree with the Zara dissent because nothing in Section 1003.1(e)(4) suggests that it is intended to do away with the statutory requirement of exhaustion of administrative remedies, 8 U.S.C. § 1252(d). Even if it were so intended, we doubt that the intent of the regulation could overcome the congressionally mandated exhaustion requirement. Section 1252(d) concerns the scope of our review and is not administered by the agency. The agency therefore is not entitled to deference in interpreting it. See INS v. Aguirre-Aguirre, 526 U.S. 415, 424, 119 S.Ct. 1439, 143 L.Ed.2d 590 (1999) (stating that a court applies the principles of deference described in Chevron U.S.A., Inc. v. Natural Resources Defense Council, Inc., 467 U.S. 837, 842, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984), when confronted with questions implicating an "agency's construction of the statute which it administers"); Brissett v. Ashcroft, 363 F.3d 130, 133 (2d Cir. 2004) ("[W]e review the agency's construction of . . . federal statutes that it does not administer de novo."); Citicorp v. Bd. of Governors of Fed. Reserve Sys., 936 F.2d 66, 75 (2d Cir. 1991) ("We recognize that courts are not obliged to defer to interpretations of a statute made by agencies not responsible for its administration."). The agency can regulate the standards it applies, but not our review of agency action. In short, the streamlining regulation cannot undermine the exhaustion requirement of Section 1252(d) because the agency is not charged with implementing this statutory provision.

Petitioners, based on the Zara dissent, also argue that interpreting Section 1003.1(e)(4) as dispensing with statutory exhaustion does not conflict with Section 1252(d) because (1) Section 1252(d)(1) requires the exhaustion of only those "administrative remedies available to the alien as of right," and (2) once a BIA member determines that streamlining is appropriate, the alien has no right to plenary review, and the IJ's decision becomes the final agency decision. Zara, 383 F.3d at 933 (Tashima, J., dissenting); see also 8 C.F.R. § 1003.1(e)(4)(ii). In petitioners' view and the view of the Zara dissent, the nature of BIA streamlining review thus makes any exhaustion requirement prudential rather than jurisdictional.

We disagree. An appeal as of right to the BIA is available to any alien who is ordered removed by an IJ except those aliens who are ordered removed in absentia. See 8 C.F.R. § 1240.15. While the first step of an appeal — consideration of whether streamlining is appropriate — may result in denying the alien the right to plenary review, it is nevertheless a right to appeal within the meaning of Section 1252(d)(1). The Karajs had the right to convince the BIA that they were entitled to plenary review. This right carried with it a corresponding obligation to explain why the IJ's decision was wrong. See Zara, 383 F.3d at 931. Therefore, we lack jurisdiction to reach the Karaj's withholding-of-removal and CAT claims and must dismiss the petition for review as to those claims.

CONCLUSION

For the reasons we have discussed, we dismiss the Karajs' withholding-of-removal and CAT claims. However, we grant the petition for review in part and vacate the IJ's denial of asylum as well as the order of removal and remand to the BIA for further proceedings consistent with this opinion. Accordingly, we also vacate as unnecessary the stay of removal granted on November 3, 2004.