GORSUCH, Circuit Judge.

Alonso Garcia-Carbajal seeks to challenge a Board of Immigration Appeals ("BIA") order on grounds he never argued to the Board. Ordinarily, this a petitioner cannot do. Ordinarily, a petitioner must exhaust all administrative processes available to hear his arguments before he may seek to bring those arguments to court. But Mr. Garcia-Carbajal submits his case isn't an ordinary one. Under Sidabutar v. Gonzales, 503 F.3d 1116 (10th Cir. 2007), he says, when the BIA sua sponte considers arguments not advanced by the petitioner, the Board effectively exhausts the available administrative remedies for the petitioner, so that the petitioner may later pursue those arguments in court. Sidabutar's "sua sponte exhaustion" rule, however, is a narrow one. To qualify for it, the BIA must: (1) clearly identify a claim, issue, or argument not presented by the petitioner; (2) exercise its discretion to entertain that matter; and (3) explicitly decide that matter in a full explanatory opinion or substantive discussion. Only then may a petitioner take an argument to court that he never pursued before the BIA. Because none of these three circumstances exists here, we cannot say Mr. Garcia-Carbajal exhausted his administrative remedies and so dismiss his petition for review.

I

This case began when the Department of Homeland Security sought to remove Mr. Garcia-Carbajal from the country. In response, Mr. Garcia-Carbajal conceded that he entered the country without inspection and was lawfully subject to removal. At the same time, though, he sought discretionary relief under 8 U.S.C. § 1229b(b). That provision allows the Attorney General to "cancel" a removal that would result in "unusual hardship" to an alien's U.S. citizen family members. In support of his cancellation request, Mr. Garcia-Carbajal testified to economic and personal harms that would befall his family should he be forced to leave the country.

But an immigration judge ("IJ") hearing Mr. Garcia-Carbajal's case under the Attorney General's delegated authority saw a problem. Section 1229b(b) prohibits the Attorney General from cancelling the removal of an alien who has been convicted of a "crime involving moral turpitude." See 8 U.S.C. § 1229b(b)(1)(C); 8 U.S.C. § 1182(a)(2). And this posed an obstacle for Mr. Garcia-Carbajal, the IJ held, given his prior conviction for assault under Colo. Rev. Stat. § 18-3-204. Noting that Mr. Garcia-Carbajal's conviction involved "knowingly causing bodily injury," the IJ found that this qualified as a "crime involving moral turpitude" and so ruled Mr. Garcia-Carbajal ineligible for cancellation. R.O.A. at 51.

Mr. Garcia-Carbajal filed a terse appeal in the BIA. His argument there focused not on the substantive question whether his prior state conviction was or wasn't a crime involving moral turpitude, but on the process the IJ used to analyze that question. Other than another theory he's since abandoned, the sum total of Mr. Garcia-Carbajal's appeal was this:

The trial court failed to engage in the analysis described in the BIA decision in Silva-Trevino, [ 24 I. N. Dec. 687, 2008 WL 4946455 (A.G. 2008)], and therefore, its analysis is flawed. That decision was issued after the [immigration judge's] decision herein, and therefore, the court could not be expected to have been aware of it before it existed, but nonetheless, that decision is binding precedent, and the court is required to follow it.

R.O.A. at 17. In Matter of Silva-Trevino, the Attorney General held that an immigration judge should first look at the statute of conviction to determine whether there is a "realistic probability" that the statute will sometimes reach conduct involving moral turpitude. 24 I. N. Dec. at 698. If the statute always or never applies to such conduct, the inquiry ends. But if that inquiry doesn't resolve the question, the immigration judge should then look to the record of conviction to determine whether the petitioner's specific conviction involved moral turpitude. Id. at 698-99.

The BIA rejected Mr. Garcia-Carbajal's appeal. Acknowledging that Silva-Trevino hadn't yet been decided at the time of the IJ's decision in Mr. Garcia-Carbajal's case, the BIA held that the IJ nonetheless had anticipated and "essentially . . . followed" the path Silva-Trevino later suggested. R.O.A. at 3-4. The immigration judge had determined that the Colorado statute "reached both crimes that involve moral turpitude and those that do not. He then . . . examined the conviction records which indicate . . . that [Mr. Garcia-Carbajal's] conviction involved knowingly causing bodily injury to another individual. As such the Immigration Judge correctly determined that the crime involved moral turpitude. See Matter of Solon, 24 I. N. Dec. 239 (BIA 2007), citing Matter of Fualaau, 21 I. N. Dec. 475 (BIA 1996)." R.O.A. at 4. In this way, the BIA concluded, the immigration judge had proceeded consistently with Silva-Trevino and reached the correct result. Id.

II

In his petition for review before us, Mr. Garcia-Carbajal no longer disputes that his case was analyzed under the process suggested by Silva-Trevino. Instead, he seeks to pursue two substantive arguments why his crime doesn't qualify as one "involving moral turpitude." First, he says, as a categorical matter the statute under which he was convicted never implicates crimes of moral turpitude. Second, and even if it does, he says his conviction shouldn't be considered a crime involving moral turpitude because it didn't require the state to prove that he acted with a specific intent or inflicted serious bodily injury. See Petr. Br. at 12 (Statement of the Issues Presented). We lack authority to entertain these, arguments, however, because Mr. Garcia-Carbajal never pursued them before the BIA and so failed to exhaust them administratively. Neither are we persuaded by Mr. Garcia-Carbajal's suggestion that Sidabutar excuses his failure to exhaust.

A

It is a fundamental principle of administrative law that an agency must have the opportunity to rule on a challenger's arguments before the challenger may bring those arguments to court. "A reviewing court usurps the agency's function when it sets aside the administrative determination upon a ground not theretofore presented and deprives the [agency] of an opportunity to consider the matter, make its ruling, and state the reasons for its action." Unemp. Comp. Comm'n of Alaska v. Aragon, 329 U.S. 143, 155, 67 S.Ct. 245, 91 L.Ed. 136 (1946). The purposes behind this rule are many and important: to avoid premature interference with agency processes, to give the agency the opportunity to correct its own errors, and to afford the parties the benefits of whatever expertise the agency may possess. See Weinberger v. Salfi, 422 U.S. 749, 765, 95 S.Ct. 2457, 45 L.Ed.2d 522 (1975); Sidabutar, 503 F.3d at 1121. For all these reasons, we often refuse to consider arguments — sometimes very good arguments — that were not presented to the agency before being presented to us. See Micheli v. Dir., OWCP, 846 F.2d 632, 635 (10th Cir. 1988).

This general principle of administrative law bears special force in the immigration context, where Congress has reduced it to a statutory command. See 8 U.S.C. § 1252(d) (an alien seeking, as here, to challenge a removal order may do so "only if [] the alien has exhausted all administrative remedies available to" him). It is not enough to go through the procedural motions of a BIA appeal, or to make "general statements in the notice of appeal to the BIA," or to level "broad assertions" in a filing before the Board. See Torres de la Cruz v. Maurer, 483 F.3d 1013, 1018 (10th Cir. 2007). To satisfy § 1252(d)(1), an alien must present the same specific legal theory to the BIA before he or she may advance it in court.

Our decision in Torres de la Cruz illustrates the point. There, a legally admitted alien faced removal because he stood convicted of a "controlled substance" offense. See 8 U.S.C. § 1227(a)(2)(B)(i). He appealed to the BIA, arguing that his conviction wasn't a controlled substance offense because it was only a misdemeanor. Before this court he urged the same conclusion, but changed his argument. Now, he said, his conviction was not a controlled substance offense because it involved drug possession, not drug trafficking as required under his interpretation of the statute. We held this latter theory had not been exhausted administratively and refused to consider it on the merits. See Torres de la Cruz, 483 F.3d at 1018. It was not enough for the petitioner to challenge the classification of his conviction before the BIA; we held that he had to present to the BIA the specific legal theory why the government's classification was incorrect.

Under this standard, Mr. Garcia-Carbajal has not exhausted the arguments he seeks to pursue in this court. The only question he presented for decision to the BIA was whether the immigration judge "failed to engage in the [two step] analysis described in the BIA decision in Silva-Trevino." R.O.A. at 17. Before us, he has abandoned this particular legal theory entirely. Instead of challenging the process by which his case was analyzed, he now seeks to challenge the substance of the results it reached — arguing first, as a categorical matter, that the Colorado statute under which he was convicted never implicates crimes of moral turpitude; and, second, that, even if the statute does sometimes implicate crimes of moral turpitude, his particular conviction wasn't such a crime. Neither of these specific legal theories was ever presented to the BIA. Of course, Mr. Garcia-Carbajal did ask the BIA to reverse the immigration judge's decision. But presenting a conclusion or request for relief to the BIA isn't enough to exhaust every potential argument for reaching that conclusion or winning that relief. Under § 1252(d)(1) and Torres de la Cruz, Mr. Garcia-Carbajal had a duty to present to the BIA all of his specific legal theories for reversal. This he did not do, and he may not add new theories seriatim as the litigation progresses from the agency into the courts.

B

Even if all this ordinarily holds true, Mr. Garcia-Carbajal submits his is no ordinary case. We may, he says, review his new arguments on appeal because of a rule we announced in Sidabutar. There, this court recognized that "generally [we will] assert jurisdiction only over those arguments that [an alien] properly presents to the BIA." Sidabutar, 503 F.3d at 1118. But we then proceeded to recognize a very narrow caveat. And it is this caveat Mr. Garcia-Carbajal seeks to exploit. We don't think he can.

To understand why, some background about Sidabutar is necessary. There, the alien appealed to the BIA only his political asylum claim. In its decision, the Board proceeded to dispose not only of that claim for relief; it also expressly reached out and considered the alien's (never appealed) claims involving restriction on removal and the convention against torture, issuing a final substantive decision on those two independent claims for relief as well. Id. While Article III courts don't usually reach out to decide unappealed claims for relief, agencies aren't always subject to the same strictures. And precisely because of the deference we owe agencies when they are interpreting their own administrative procedures, we said that "if the BIA deems an issue sufficiently presented to consider it on the merits, such action by the BIA exhausts the issue as far as the agency is concerned . . . and that is all § 1252(d)(1) requires." Sidabutar, 503 F.3d at 1120. The question of exhaustion is ultimately a procedural one, we acknowledged, and administrative agencies "should be free to fashion their own rules of procedure" for deciding when a matter is or isn't exhausted. Id., citing FCC v. Pottsville Broad. Co., 309 U.S. 134, 143, 60 S.Ct. 437, 84 L.Ed. 656 (1940). If the BIA decides an argument is worth sua sponte taking up and issuing a final agency decision on, thereby exhausting all available agency processes to hear and resolve that argument, we will not stand in its way.

At the same time, we acknowledged that this form of exhaustion will be the rare exception, not the rule. It isn't every day, after all, that an agency takes up two independent claims for relief not appealed to it and proceeds to issue a final decision on their merits. So in Sidabutar we stressed that it is only when it is clear that the BIA has issued "a full explanatory opinion or a discernible substantive discussion" on the merits of "matters not presented by the alien" that we will consider it to have chosen to exhaust that claim administratively. 503 F.3d at 1122. After all, we must still and always ensure § 1252(d)(1)'s exhaustion requirement has been met — that an argument has been aired and finally resolved by the agency; that we aren't prematurely interfering with a matter the BIA has yet to consider fully and address squarely.

To satisfy the exhaustion requirement in the narrow fashion Sidabutar suggests, then, we hold three preconditions must be met to qualify for exhaustion under its terms. As in Sidabutar itself, the BIA's ruling must: (1) clearly identify a claim, issue, or argument not presented by the petitioner; (2) demonstrate that the agency chose to exercise its discretion to entertain that matter; and (3) explicitly decide that matter in a full explanatory opinion or substantive discussion.

Each of these requirements is essential. If it's not clear that the agency identified a potential argument, we can hardly be sure that the agency was aware of it, let alone ruled on it. Whenever an agency states a conclusion (as here, for example, "the Immigration Judge correctly determined that the crime involved moral turpitude") it impliedly rejects any number of unmade potential arguments. But that doesn't mean the agency noticed those arguments, let alone considered and ruled on them. Likewise, even if the agency identifies a potential argument (unmade by the petitioner), we can't be certain the agency applied its expertise to the question unless and until the agency makes clear its wish to entertain the argument and proceeds to rule on it in a full explanatory opinion or substantive discussion. Only when all of these conditions are met can we be sure that § 1252(d)(1)'s exhaustion requirement has been satisfied, with the agency having had a fair chance to apply its expertise to the matter and having reached a final decision.

The whole point of Sidabutar was to respect an agency's clearly expressed wish to exhaust a question not presented to it by reaching a final decision — to defer to an agency's chosen administrative exhaustion procedures. If stray or cryptic comments by an agency in the course of its decision were enough to invoke our jurisdiction over arguments never raised before the agency, litigants would have less incentive to bring all their arguments first and clearly to the agency for decision. Worse, the agency itself would be inhibited from providing thorough and explanatory opinions, as any passing remark could serve as the basis for the alien's next round of appeal. In this way, the opportunity for a reasoned and expert agency decision in the first instance would be much diminished. To ensure that we are enforcing the exhaustion requirement in a way respectful to agency processes — rather than snaring the agency — we may only proceed to consider an issue under Sidabutar when it is clear that the Board actually considered the question and applied its expertise to answer it.

None of the requisite clarity exists in this case. The closest thing we have to evidence that the BIA identified and addressed Mr. Garcia-Carbajal's newly minted substantive arguments is this language at the end of its opinion:

As such, the Immigration Judge correctly determined that the crime involved moral turpitude. See Matter of Solon, 24 I. N. Dec. 239 (BIA 2007), citing Matter of Fualaau, 21 I. N. Dec. 475 (BIA 1996).

BIA Op. at 2. Because Solon and Fualaau spoke to when a crime is and isn't one "involving moral turpitude," we suppose it's possible the BIA anticipated the substantive question whether Mr. Garcia-Carbajal's crime qualified and decided that it did. But it's also possible the Board didn't.

In the first place, the only issue the BIA clearly identified in this case was the question actually presented to it — whether the IJ successfully anticipated and followed Silva-Trevino's analytical process. The agency did not, for example, take a detour to note that "although we have previously held that purposeful assault is a crime involving moral turpitude, knowing assault is a lesser mens rea arguably calling for a different result." That would've signaled that the agency recognized that an alien might try (as Mr. Garcia-Carbajal tries in one of his arguments before us) to distinguish between purposeful and knowing assaults — and would've opened the possibility that the agency was about to provide a considered answer to the question. But no such language exists in the BIA's opinion.

Likewise, nothing in the BIA's opinion demonstrates that the agency exercised its discretion to take up that or any other of the arguments Mr. Garcia-Carbajal now seeks to press in court. The Board merely walked through the steps necessary to answer Mr. Garcia-Carbajal's objection that the immigration judge improperly applied Silva-Trevino's two-step analysis. Stray statements made in the course of answering the arguments the alien actually presented do not, without more, indicate that the agency sought to exercise its discretion to do anything beyond what was asked of it.

Finally, nothing in the BIA's opinion could be called a full explanatory opinion or substantive discussion deciding Mr. Garcia-Carbajal's current arguments. While we of course defer to the agency's determination of the depth of explanation merited by a given question, one cryptic sentence followed by two citations to prior authority cannot be fairly characterized explanatory or substantive.

Simply put, Mr. Garcia-Carbajal meets none of the three essential elements to exhaustion under Sidabudar. Allowing him to avoid a statutory exhaustion requirement based on language of, at most, ambiguous purpose would do nothing to respect agency authority and much to undermine it, encouraging future efforts by litigants to squeeze elephants of arguments into court through administrative mouseholes. This is not the sort of respect for administrative decisionmaking on which § 1252(d), Torres de la Cruz, and Sidabutar are grounded and which they seek to encourage.

Because Mr. Garcia-Carbajal has not exhausted his administrative remedies on the arguments he now seeks to pursue in this court, the petition for review is

Dismissed.