
555 F.3d 1089 (2009)
Jorge Arturo SOTO-OLARTE; Maria Jesus Esteves-La Torre, Petitioners,
v.
Eric H. HOLDER, Jr., Attorney General, Respondent.
No. 06-71822.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted May 9, 2008.
Filed February 23, 2009.
*1090 Edgardo Quintanilla, Quintanilla Law Firm, Sherman Oaks, CA, for the petitioners.
Joshua P. Jones, United States Department of Justice, Washington, D.C., for the respondent.
Before: JOHN T. NOONAN, WILLIAM A. FLETCHER, and RONALD M. GOULD, Circuit Judges.
GOULD, Circuit Judge:
Jorge Arturo Soto-Olarte and his wife Maria Jesus Esteves-La Torre petition for review of the Board of Immigration Appeals' ("BIA") opinion dismissing their appeal of an immigration judge's ("IJ") denial of their petitions for asylum, withholding of removal, and protection under the United Nations Convention Against Torture ("CAT"). We grant the petition for review and remand this case to the BIA for further proceedings, but we hold that on remand the BIA need not necessarily deem Soto-Olarte credible.

I
Jorge Arturo Soto-Olarte ("Soto-Olarte"), and his wife Maria Esteves-La Torre ("La Torre"), natives and citizens of Peru, sought asylum and withholding of removal based on alleged persecution by the terrorist organization Shining Path. The incident central to Soto-Olarte's claim occurred on June 19, 2003. According to Soto-Olarte's testimony, two members of the Shining Path broke into his house in Peru, while two other Shining Path members remained outside. Soto-Olarte fired his gun in the air, triggering his car alarm, and the four individuals fled.
Soto-Olarte submitted a police report mentioning this incident, but the report as produced by the police differs from Soto-Olarte's account of the incident. The police report stated that Soto-Olarte was awakened by his car alarm, and when he went outside two security guards told him they saw two individuals fleeing over the wall. The report said nothing about two other people entering Soto-Olarte's house, about a gun being fired, or about any involvement by the Shining Path. Finally, the police report recited that Soto-Olarte had said items were stolen from his car, while Soto-Olarte's own account in his testimony and in his declaration mentions no property loss.
Soto-Olarte and La Torre were charged as removable in 2004. They conceded removability but sought relief in the form of asylum, withholding of removal, and protection under the CAT. At the IJ hearing Soto-Olarte's direct examination testimony focused on the June 2003 incident. Neither the government nor the IJ asked Soto-Olarte about the contents of the police report. Before testifying, in a written declaration filed with the immigration court, Soto-Olarte had explained that the police report did not mention the Shining Path because, as he put it, the police "did *1091 not want to get involved with allegations of the Shining Path." Soto-Olarte did not explain in his written declaration, nor in his hearing testimony, why the police report did not mention the home invasion or gunfire that he described in his hearing testimony.
The IJ denied Soto-Olarte's and La Torre's petition, finding that Soto-Olarte was not credible because his testimony about the June 2003 incident differed from the account in the police report. The IJ then held alternatively that even if Soto-Olarte's testimony was credible, she would still have denied relief on the ground that Soto-Olarte failed to show past persecution or a well-founded fear of future persecution because "[t]he June 2003 incident appears to be a criminal robbery." The BIA affirmed the IJ's ruling and alternate holding, citing the same inconsistencies between Soto-Olarte's testimony and the police report.

II

A
We review the IJ and BIA's adverse credibility finding for substantial evidence. See Kaur v. Ashcroft, 379 F.3d 876, 884 (9th Cir.2004). The IJ based her adverse credibility finding on the inconsistencies between Soto-Olarte's account, during his immigration proceeding, of the June 2003 incident as a terrorist home invasion and the police report describing the same event as a car burglary. These inconsistencies go to the heart of the petitioners' claim. See Desta v. Ashcroft, 365 F.3d 741, 745 (9th Cir.2004). However, Soto-Olarte gave a plausible explanation in his declaration for one of these inconsistencies  the police report's failure to mention the Shining Path. The IJ "did not comment on [this] explanation [in her decision], nor suggest any reason that [she] found his explanation not credible." Garrovillas v. INS, 156 F.3d 1010, 1013 (9th Cir.1998). This lack of consideration given to Soto-Olarte's proffered explanation was error and prevents the underlying inconsistency from serving as substantial evidence to support the IJ's adverse credibility finding. See, e.g., Kaur, 379 F.3d at 884 ("An adverse credibility finding is improper when an IJ fails to address a petitioner's explanation for a discrepancy or inconsistency."); Guo v. Ashcroft, 361 F.3d 1194, 1201 (9th Cir.2004) (holding that an alleged inconsistency in a petitioner's testimony could not serve as substantial evidence for an adverse credibility finding where the IJ "did not address at all [the petitioner's] reasonable and plausible explanation" for the inconsistency).
The BIA made only passing and incomplete mention of Soto-Olarte's explanations for the discrepancies, noting that "[t]he respondents argue that this was a minor inconsistency or no consistency [sic] at all" but concluding that "[w]e disagree." Because the BIA's opinion does not refer to the explanation that Soto-Olarte gave, to the effect that police in Peru are reluctant to mention the Shining Path, and does not give the BIA's reasons for considering that explanation unpersuasive, the BIA's treatment of Soto-Olarte's explanation does not satisfy our precedential requirement that "in order to ensure a fair hearing, the BIA not only identify specific inconsistencies, but also `address in a reasoned manner the explanations that [the petitioner] offers for these perceived inconsistencies.'" Campos-Sanchez v. INS, 164 F.3d 448, 450 (9th Cir.1999) (quoting Osorio v. INS, 99 F.3d 928, 933 (9th Cir. 1996)). We hold that where Soto-Olarte gave an explanation of inconsistencies between his account of the June 2003 incident at his home and the account of that incident in the police report, those inconsistencies cannot serve as substantial evidence for a finding that Soto-Olarte was *1092 not credible when neither the IJ nor the BIA addressed Soto-Olarte's explanation "in a reasoned manner." Id.
Soto-Olarte's explanatory statement does not account for all of the inconsistencies between the police report and Soto-Olarte's testimony. His explanation does not suggest why the police report did not mention that there were two intruders inside the house as well as two outside of it, nor does it suggest that Soto-Olarte shot his gun to scare the men away. Moreover, his explanation sheds no light on why the police would report that a bag containing sales slips and toys was stolen from Soto-Olarte's car when Soto-Olarte in his written statement and during his testimony did not mention any property being taken. However, Soto-Olarte was never asked about any of these inconsistencies at his hearing before the IJ. It is speculative at this juncture, but certainly possible that Soto-Olarte may have had good explanations for the remaining differences between his testimonial report and that filed by the police and also possible that the BIA might have good reasons to reject his explanations. It may be that Soto-Olarte's explanation that the police don't like to mention the Shining Path also explains why they would not mention his use of a gun or the home invasion, because these points were part of his story about the Shining Path. In any event, the IJ could not properly base her adverse credibility determination on the inconsistencies between Soto-Olarte's testimony and the police report that Soto-Olarte did not explain in his declaration, when she did not ask Soto-Olarte about these discrepancies or give him an opportunity to reconcile them. See Don v. Gonzales, 476 F.3d 738, 741 (9th Cir.2007) ("[T]he IJ `must provide a petitioner with a reasonable opportunity to offer an explanation of any perceived inconsistencies that form the basis of a denial of asylum.'" (quoting Ordonez v. INS, 345 F.3d 777, 786 (9th Cir.2003))); Chen v. Ashcroft, 362 F.3d 611, 618 (9th Cir.2004) (finding that the petitioner "was denied a reasonable opportunity to explain what the IJ perceived as an inconsistency in her testimony" and concluding that "[t]he IJ's doubt about the veracity of her story, therefore, cannot serve as a basis for the denial of asylum").[1] Because the IJ did not offer Soto-Olarte an opportunity to explain the inconsistencies on which she later relied in finding him not credible and did not address the explanation he gave for some of those inconsistencies, the IJ's adverse credibility finding, which was subsequently adopted by the BIA, was not supported by substantial evidence.
The IJ and BIA alternately held that even if Soto-Olarte were deemed credible, he and his wife still had not met their burden of establishing eligibility for asylum or withholding of removal. Despite the asserted independence of this conclusion, however, neither the IJ nor the BIA took all of Soto-Olarte's testimony as true for the purposes of determining his and La Torre's eligibility for asylum, as they are required to do when deeming a petitioner to be credible in an alternate holding. See *1093 Kalubi v. Ashcroft, 364 F.3d 1134, 1137 (9th Cir.2004) ("Testimony must be accepted as true in the absence of an explicit adverse credibility finding."). In reaching the conclusion that the experiences Soto-Olarte had suffered in Peru did not rise to the level of persecution on the basis of a protected ground, both the IJ and BIA referred to the June 2003 incident as a "criminal robbery," thus crediting the police report's version of what happened that night instead of accepting the version offered by Soto-Olarte that his home was invaded by Shining Path terrorists who were motivated to threaten or harm Soto-Olarte because of his political views. This alternate holding of the BIA and IJ is not controlling, because its explicit reasoning relied on an adverse credibility determination that we have determined is not supported by substantial evidence.

B
There have been cases in our circuit in which, after determining that an adverse credibility finding is not supported by substantial evidence, we have directed the BIA on remand to make additional determinations, but required the agency to accept the petitioner's testimony as true. See, e.g., Guo, 361 F.3d at 1203-04 ("Where an appellate court has held that an IJ's or BIA's adverse credibility finding is not supported by substantial evidence... the proper procedure is to remand the case to the BIA for further consideration and investigation in light of the ruling that the petitioner is credible."); He v. Ashcroft, 328 F.3d 593, 604 (9th Cir.2003). However, no other circuit has adopted this "deemed credible" rule.[2]See, e.g., Castaneda-Castillo v. Gonzales, 488 F.3d 17, 24-25 (1st Cir.2007) (en banc) ("The suggestion may be made ... [citing He] that remand gives the agency a second bite at the apple. The short answer is that, outside criminal prosecutions governed by double jeopardy principles, second bites are routine in litigation. If the agency decision is flawed by mistaken legal premises, unsustainable subsidiary findings, or doubtful reasoning, remanding to give the agency an opportunity to cure the error is the ordinary course."); Li v. INS, 453 F.3d 129, 136 (2d Cir.2006) ("[W]hen we find fault with an adverse credibility finding, we will not substitute our own judgment for the agency's, but ordinarily will remand to the agency for additional explanation or investigation." (internal quotation marks omitted)); Elzour v. Ashcroft, 378 F.3d 1143, 1154 (10th Cir.2004) ("[W]e are not finding [Petitioner] credible. Rather, we are concluding ... that because of the lack of substantial evidence to support the *1094 adverse credibility determination, we will remand in order for the agency to further explain or supplement the record." (quoting Dia v. Ashcroft, 353 F.3d 228, 260 (3d Cir.2003))).
Our deemed credible rule has never been described by us as being absolute in its application, nor has it been practically applied in that fashion. Before our decision in He v. Ashcroft, we often remanded an adverse credibility finding on an open record to allow the BIA to reconsider a petitioner's credibility. E.g., Paramasamy v. Ashcroft, 295 F.3d 1047, 1054-55 (9th Cir.2002) ("We cannot uphold the adverse credibility finding ... [and] remand for a new hearing, with an individualized determination of credibility."); Campos-Sanchez, 164 F.3d at 450 ("This matter is remanded for proceedings at which [the petitioner] may respond to the perceived inconsistencies, offer explanations, and be heard on his credibility."). Before He, we also had some cases applying the deemed credible rule on remand. See, e.g., Akinmade v. INS, 196 F.3d 951, 958 (9th Cir. 1999) ("As in other similar cases, under these circumstances, we deem the petitioner's testimony credible."); Aguilera-Cota v. INS, 914 F.2d 1375, 1383 ("Other than the minor omission and the other insignificant reasons given by the IJ, there is in the case before us a total absence of contradictory evidence in the record as a whole that potentially undermines [the petitioner's] credibility. Under these circumstances, we accept the testimony as true."); Damaize-Job v. INS, 787 F.2d 1332, 1338 (9th Cir.1986) ("We presume that if the IJ had any additional reasons to doubt [the petitioner's] credibility, the IJ would have stated so in the decision below. Because the IJ expressed no further concerns, and the only explicitly articulated reasons rested on impermissible factors, then we conclude from the IJ's opinion that [the petitioner] was an otherwise credible witness."). After He, we have still in appropriate cases declined to apply that rule when we have concluded that the total circumstances favored remanding on an open record for a new determination of credibility. For example, we have allowed the BIA on remand to reconsider a petitioner's credibility in a new hearing when an IJ "denied Petitioner a reasonable opportunity to present evidence on her behalf." Kaur v. Ashcroft, 388 F.3d 734, 737 (9th Cir.2004). In such cases "[w]e do not suggest that the agency was or is required to credit Petitioner's version of events uncritically" on remand. Lopez-Umanzor v. Gonzales, 405 F.3d 1049, 1059 (9th Cir. 2005).
We applied the deemed credible rule in He because the BIA "should not have repeated opportunities to show that [the petitioner] is not credible any more than [the petitioner], had he lost, should have an opportunity for remand and further proceedings to establish his credibility." He, 328 F.3d at 604. He, however, did not involve a situation where the IJ or BIA failed to ask the petitioner about inconsistencies going to the heart of the petitioner's claim, or failed to address the explanations a petitioner offered for inconsistencies. Instead, in He we rejected the IJ and BIA's adverse credibility findings, stating that "[the IJ] was impatient, hostile, and hectoring in his questions, and he was careless and unjustified in his conclusions" and "the BIA's reason [for finding adverse credibility] is no stronger than any of the IJ's." Id. at 603.
In He, the IJ provided three reasons ostensibly supporting his adverse credibility finding. On appeal, the BIA added a fourth reason. Id. We held that all four reasons were unsupported by the evidence in the record. The circumstances of He suggest that the deemed credible rule may apply when it is evident that the IJ and BIA have both strained to provide reasons *1095 properly supporting an adverse credibility finding, but despite their best efforts have been unable to do so. Here, however, there are inconsistencies that go to the heart of Soto-Olarte's claim and the crux of the question is whether Soto-Olarte can satisfactorily explain those inconsistencies.
Because the three-judge decision in He could not have overruled our prior precedents in which we did not apply the deemed credible rule, following those prior precedents and the later precedents with open record remands after He remains an option: He represents one instance in which we decided the deemed credible rule was desirable, but He does not require us to apply the deemed credible rule in all future cases, whatever their circumstances. Our precedent grants us discretion to apply the deemed credible rule in appropriate cases like He and its predecessors, or not to apply the deemed credible rule by remanding on an open record when we conclude that is the more sensible result under all the circumstances.
Stated another way, we can see some differences in the fact patterns presented in cases where we remanded with directions that the petitioner be deemed credible, and those where we remanded for unbounded determinations on an open record. If it is apparent from the record before us that the IJ and BIA have listed all possible reasons to support an adverse credibility determination, and they are inadequate in law or not supported by substantial evidence, then there may be cases where on remand we can sensibly say that a petitioner should be deemed credible. But, conversely, if there is a reasonable prospect from the administrative record that there may be additional reasons upon which the IJ or BIA could rely, then it is appropriate to remand in a way that permits the agency to provide those reasons. In all of this we are somewhat hemmed in by our limited role in administrative review of agency decisions, so that in any case in which there are doubts about whether there may be other grounds for rejecting credibility, we should not restrict the BIA or an IJ.
We do not in this case attempt to articulate a definitive and all-encompassing rule as to when the deemed credible rule may be applied and when it must be rejected. After the normal common-law process of inclusion and exclusion that occurs over many cases, we may want to fashion a more definitive statement. It is sufficient for our purposes here to conclude that both the option of deeming a petitioner credible and the option of remanding on an open record remain viable in an appropriate case.
Here, we conclude that it is appropriate that the BIA be allowed on remand to reexamine Soto-Olarte's credibility. Applying the deemed credible rule when the IJ and BIA did not allow Soto-Olarte the opportunity to explain inconsistencies going to the heart of his claim would grant excessive deference to Soto-Olarte's future and now unknown explanations of the perceived inconsistencies. If the BIA were forced to deem Soto-Olarte's testimony credible on remand, whatever he says, Soto-Olarte would never have to give plausible explanation for the inconsistencies between his testimony and the police report, even though these inconsistencies go to the heart of his claim. And if we apply a deemed credible rule and Soto-Olarte then gives an implausible explanation of these inconsistencies, the BIA would have to accept it as true. We see no valid reason to hold that the BIA erred in not giving Soto-Olarte a chance to explain inconsistencies, yet then order the agency on remand to credit Soto-Olarte whatever he says. In our view, it will most assuredly lead to a more rational implementation of immigration law and policy if the petitioner *1096 is required to explain inconsistencies and if the BIA can then make credibility determinations in light of the supplemented record. We hold that the BIA need not necessarily deem credible Soto-Olarte's explanation of the as-yet-unexplained inconsistencies between his testimony and the police report of the June 2003 incident.
Applying the deemed credible rule also makes little sense when we reject a ground for adverse credibility because the IJ did not address a petitioner's explanation of an inconsistency that goes to the heart of the petitioner's claim. The BIA and IJ erred when they did not explain why they rejected Soto-Olarte's explanation for the police report's failure to mention the Shining Path. To apply the deemed credible rule, however, would deny the agency an opportunity to answer with its view of Soto-Olarte's explanation. If the BIA had a valid reason for rejecting Soto-Olarte's explanation and merely neglected to include it in its decision, then we should allow the agency to present that reason on remand rather than flatly decree that Soto-Olarte is credible. See INS v. Ventura, 537 U.S. 12, 16, 123 S.Ct. 353, 154 L.Ed.2d 272 (2002) (stating that when reversing the BIA, "the proper course, except in rare circumstances, is to remand to the agency for additional investigation or explanation" (emphasis added)).
Considering all of the circumstances, we have concluded that applying the deemed credible rule in this case would create illogical results on remand and preclude a decision on the basis of the full record that will be presented to the BIA after further proceedings on remand. Accordingly, we hold that the BIA on remand need not necessarily deem credible the petitioner's testimony when we have remanded because the petitioner was not asked about inconsistencies, or because the IJ did not address the petitioner's explanation of perceived inconsistencies.

III
The IJ and BIA's adverse credibility determination was not supported by substantial evidence. We remand on an open record to give the agency the opportunity to evaluate Soto-Olarte's credibility while allowing him to explain as-yet-unexplained inconsistencies concerning the June 2003 incident and while considering the explanations that he has already provided. Because the BIA has not evaluated Soto-Olarte's and La Torre's eligibility for asylum or withholding of removal independently from its adverse credibility finding, we also remand to give the agency an opportunity to make those determinations in the first instance. We do not remand the petitioners' CAT claim, because that claim was not presented as part of this appeal. See Smith v. Marsh, 194 F.3d 1045, 1052 (9th Cir.1999) ("[O]n appeal, arguments not raised by a party in its opening brief are deemed waived.").
PETITION FOR REVIEW GRANTED; CASE REMANDED IN PART.
NOTES
[1]  Although we conclude that the absence of an opportunity to explain inconsistencies was one reason that the IJ's adverse credibility finding was not supported by substantial evidence, we reject Soto-Olarte's related argument that the lack of inquiry about those inconsistencies at the hearing violated due process, given that Soto-Olarte had an opportunity to offer explanations for those inconsistencies or otherwise dispute the adverse credibility finding in his appeal to the BIA. Cf. Campos-Sanchez, 164 F.3d at 450 (holding in the context of a due process analysis that "[w]hen the BIA decides a case based on an independent, adverse, credibility determination, contrary to that reached by the IJ, it must give the petitioner an opportunity to explain any alleged inconsistencies that it raises for the first time." (emphasis added)).
[2]  Our deemed credible rule is distinct from a closely related procedure that we follow when the BIA or IJ finds the petitioner not credible and then makes an alternate holding that even if the petitioner's testimony were true he or she still should be denied relief for some other reason, such as a failure to establish past persecution. In those cases, if we hold that the adverse credibility finding was not supported by substantial evidence, we deem the petitioner credible for the limited purpose of reviewing the alternate holding, as did the agency in making that holding. See, e.g., Zhu v. Mukasey, 537 F.3d 1034, 1043 (9th Cir. 2008); Mousa v. Mukasey, 530 F.3d 1025, 1029 (9th Cir.2008); Singh v. Gonzales, 439 F.3d 1100, 1111 (9th Cir.2006); Guo, 361 F.3d at 1202-03; Bandari v. INS., 227 F.3d 1160, 1168 (9th Cir.2000). Otherwise, we could not accept the alternate holding and deny the petition, because a denial would be based in part on the erroneous adverse credibility finding. If we reject the BIA's alternate holding, only then do we remand and possibly apply the deemed credible rule. E.g., Zhu, 537 F.3d at 1045; Mousa, 530 F.3d at 1030. Nothing in our analysis of the deemed credible rule, which we sometimes apply on remand, impacts this related practice, which we apply only when reviewing an alternate holding. Our holding today is not inconsistent with this line of cases, which presents an analytically distinct posture.
