Judge JACOBS dissents in a separate opinion.
STRAUB, Circuit Judge.
Petitioner Shobinder Gill petitions for review of a Board of Immigration Appeals (“BIA”) opinion finding Gill removable based on a conviction of a “crime involving moral turpitude” (“CIMT”) under 8 U.S.C. § 1227(a)(2)(A)®. Gill argues that his crime of conviction, attempted reckless assault under New York Penal Law § 120.05(4), is not a CIMT because it requires only a reckless state of mind, whereas some positive intent is required for a CIMT. Gill does not specifically argue that his conviction for attempted reckless assault does not demonstrate the requisite mental state for a CIMT because it incoherently combines the specific intent element of criminal attempt under New York law with the recklessness standard of § 120.05(4). Nonetheless, we exercise our discretion to consider this subsidiary issue sua sponte and find that the BIA committed clear error in ordering Gill’s removal based on a crime that, because it is legally impossible, demonstrates no clear mental state.
The legal incoherence of Gill’s crime of conviction was not argued in the administrative proceedings below. However, this argument is subsidiary to the general argument Gill did make before the BIA: that his crime of conviction did not reflect a sufficiently culpable mental state to be designated a CIMT. Therefore, we hold that our basis for reversing the BIA’s decision is not precluded by the exhaustion requirement for immigration appeals, 8 U.S.C. § 1252(d)(1), which provides that “[a] court may review a final order of removal only if ... (1) the alien has exhausted all administrative remedies available to the alien as of right,” or by any judicial exhaustion doctrine. Accordingly, we reverse the BIA’s order of removal, and remand with instructions to close Gill’s removal proceedings.
BACKGROUND
Gill, whose father is a United States citizen, was admitted to the United States as a visitor in 1989, at age nine, and later granted lawful permanent resident status in 1994. On June 24, 1999, Gill pleaded guilty to attempted assault in the second degree in violation of New York Penal Law (“N.Y.P.L.”) § 120.05(4), which proscribes “recklessly causing] serious physical injury to another person by means of a deadly weapon or a dangerous instrument.” 1 He was sentenced to nine months’ imprisonment. On August 12, 1999, the Immigration and Naturalization Service (“INS”)2 filed a notice to appear, charging Gill as removable based on his attempted assault conviction, which the INS characterized as a CIMT.3 Gill argued [85]*85that his crime was not a CIMT because § 120.05(4) requires only a reckless state of mind, whereas some positive intent is required for a CIMT.
The IJ agreed with Gill in a decision dated October 11, 2000, then reversed himself on February 1, 2002, after the INS moved for reconsideration. In his later order, the IJ found that, under New York law, reckless conduct involves a conscious disregard of “a substantial and unjustifiable risk” of harm, and that this disregard can, in certain circumstances, constitute a sufficiently culpable mental state to render the offense a CIMT. The BIA affirmed by a decision issued September 2, 2003, holding that, although not all crimes of recklessness constitute CIMTs, Gill’s crime did so because it involved two aggravating factors: the serious physical injury which resulted from Gill’s conduct and his use of a deadly weapon. Although neither the BIA nor the IJ found any significance in the fact that Gill’s conviction was for attempted assault, both noted this fact in their opinions.
This appeal followed.
DISCUSSION
I. Jurisdiction
Because the specific argument on the merits which we discuss in Section III infra was not raised before the BIA, we must decide at the outset whether we have jurisdiction to consider it.
Section 1252(d)(1) of Title 8 of the United States Code provides, in pertinent part, that federal courts “may review a final order of removal only if ... the alien has exhausted all administrative remedies available to the alien as of right.” While there is no question that this exhaustion requirement, being statutory, is mandatory, a question does arise as to the level of specificity at which a claim must have been made to have been “exhausted” under § 1252(d)(1).
Various decisions by this Court have spoken to this question obliquely. In Be-harry v. Ashcroft, for example, we held that the District Court had lacked jurisdiction under § 1252(d)(1) to consider Beharry’s claim for relief under 8 U.S.C. § 1182(h) (“ § 212(h) relief’)4 because he had not previously sought § 212(h) relief from the INS. 329 F.3d 51, 62 (2d Cir.2003). Because Beharry involved a habeas petition and the law was unclear as to whether § 1252(d)(1) applies to such,5 we also considered whether the “less stringent” judicial exhaustion requirement prevented the consideration of Beharry’s § 212(h) claim. We found that it did, in part because Beharry’s failure to claim § 212(h) relief below “left sizable gaps in the factual record presented to us on appeal” such that this Court would be “hard-pressed” to decide the merits of his legal claim. Id. at 62; see also Theodoropoulos v. INS (Theodoropoulos II), 358 F.3d 162, 165-69, 174 (2d Cir.2004) (holding that § 1252(d)(1) barred habeas review where petitioner, in open court, had expressly waived his right to appeal the IJ’s decision), cert. denied, — U.S.-, 125 S.Ct. 37, 160 L.Ed.2d 34 (2004). Similarly, we held in Foster v. INS that, under § 1252(d)(1), an alien’s “generalized protestations that his removal was improper” [86]*86did not allow him to argue on appeal that his crime of conviction (first degree manslaughter) was not a “crime of violence” or “aggravated felony” under immigration law. 376 F.3d 75, 77-78 (2d Cir.2004). In so holding, we explained that a petitioner must “raise issues to the BIA in order to preserve them for judicial review.” Id. at 78 (internal quotation omitted).
While we held in Beharry that the exhaustion requirements preclude a petitioner from raising a whole new category of relief on appeal, in Foster that a petitioner must have raised an issue below to present it on appeal, and in Theodoropoulos II that the statutory exhaustion requirement precludes a petitioner from bypassing the administrative review process altogether, we have never held that a petitioner is limited to the exact contours of his argument below. To the contrary, in Restrepo v. McElroy, 369 F.3d 627 (2d Cir.2004), we held that § 1252(d)(1) did not prevent us from considering a wholly new reliance argument on appeal because Restrepo did “raise[ ] the general issue of the AEDPA’s retroactivity ... in his habeas petition, and we enjoy broad discretion to consider subsidiary legal arguments that were not specifically raised below.” Id. at 633 n. 10 (emphasis added). We used “subsidiary” in a broad sense; the reliance argument Restrepo made in his administrative proceedings was that AEDPA (which foreclosed a form of relief sought by Restrepo) should not apply retroactively to crimes committed, or convictions entered, before the law’s effective date, whereas the “subsidiary” argument he raised on appeal was that AEDPA should not apply to him because he decided, in reliance on the law pre-AEDPA, to delay his application for relief until a later date when he would be better able to demonstrate rehabilitation.
In Drax v. Reno, 338 F.3d 98, 112 n. 19 (2d Cir.2003), we similarly held that § 1252(d)(1) does not limit our review to those arguments specifically raised below. In that case, we found jurisdiction to decide Drax’s eligibility for a certain type of relief from deportation-“Ga6ri/eis% relief’-where the relief was not specifically sought before the BIA but was “merely an extension of the argument his counsel raised directly before the BIA-that the Immigration Judge erred in holding that no relief was available on account of the retroactive application of [a subsequent amendment].”6
The rule that emerges from this precedent is that § 1252(d)(1) bars the consideration of bases for relief that were not raised below, and of general issues that were not raised below, but not of specific, subsidiary legal arguments, or arguments by extension, that were not made below. Our decision in Restrepo and Drax not to interpret § 1252(d)(1) to require complete conformity between an alien’s ar[87]*87gument below and on appeal makes particular sense given that immigration law has undergone rapid changes in recent years and given the fundamental interests at stake.7 Because Gill raised below the general issue, as characterized by the IJ in his February 1, 2002 order, of whether “Attempted Assault in the 2nd degree .... involve[s] the required mens rea or a guilty corrupt mind or vicious motive” (emphasis added), we have jurisdiction to consider the specific subsidiary argument (or argument by extension) that Gill’s conviction for “attempted reckless assault” fails to meet the mental state requirement of the CIMT definition because, under New York law, such a conviction is legally incoherent.8
We further find that the judicial exhaustion doctrine would not bar consideration of a specific, subsidiary legal argument, particularly one that is purely legal and falls outside the INS’s traditional area of expertise. See McCarthy v. Madigan, 503 U.S. 140, 145-46, 112 S.Ct. 1081, 117 L.Ed.2d 291 (1992) (exhaustion concerns strongest “when the action under review involves exercise of the agency’s discretionary power or when the agency proceedings in question allow the agency to apply its special expertise,” as well as when judicial review would benefit from an administrative factual record), superceded by statute on other grounds as noted in Booth v. Churner, 532 U.S. 731, 732, 121 S.Ct. 1819, 149 L.Ed.2d 958 (2001); cf. Beharry, 329 F.3d at 62 (judicial exhaustion doctrine would bar consideration of fact-specific claim of eligibility for discretionary relief). Moreover, to the extent that Gill may have technically waived the legal incoherence argument by failing to make it below, we retain broad discretion, which we now exercise in Gill’s favor, to consider waived arguments that are purely legal. See Marrero Pichardo v. Ashcroft, 374 F.3d 46, 54 (2d Cir.2004).
Even had we found that Gill’s omission was a failure to exhaust his administrative remedies under § 1252(d)(1), we nonetheless would have assumed jurisdiction to avoid manifest injustice. This Court recently so held in Marrero Pichardo v. Ashcroft, noting that “[cjourts have historically interpreted procedural rules to prevent a fundamental miscarriage of justice.” 374 F.3d at 53; cf Sun v. Ashcroft, 370 F.3d 932, 942 n. 16 (9th Cir.2004) (“There is agreement among the circuits that have addressed the issue that exceptions do apply to § 1252(d)(1), although the contours of such exceptions remain to be fully developed.”)9
[88]*88Manifest injustice would result here were Gill to be removed without full judicial review of the correctness of his removal. As explained below, the merits of his legal incoherence argument are clear-cut in his favor, and “go[ ] to the very basis for his deportation,” Marrero Pichardo, 374 F.3d at 54. Moreover, these merits were not apparent during Gill’s administrative case and have only crystalized in a subsequent opinion by the Third Circuit interpreting New York criminal law, Knapik v. Ashcroft, 384 F.3d 84 (3d Cir.2004).10 Finally, although the record contains little description of Gill’s personal circumstances, it does indicate that Gill has lived in this country, with his United States citizen father and other family members, for sixteen years, since he was nine years old; that he has been a lawful permanent resident since 1994; and that he is an honor student who is currently enrolled in college. Taken together, these factors warrant an exception to the statutory jurisdiction requirement. See Marrero Pichardo, 374 F.3d at 54 (exercising jurisdiction, in closely analogous circumstances, based on precisely the same considerations).
The dissent suggests that Marrero Pichardo must be read narrowly because it is a “single case, decided by a panel of this Court last year,” and is in tension with Theodoropoulos II. Post. The dissent does not attempt to locate any distinction in the text of Marrero Pichardo, which is squarely on point factually. Nor do we see how it is in any tension with Theodoro-poulos II, let alone in such tension that it must be narrowed. In Theodoropoulos II, we held that an applicant who had waived all administrative appeals was barred by the exhaustion requirement from seeking judicial review, and that no exception to the exhaustion requirement arose from the fact that his legal argument was, at the time he waived his administrative appeal, contrary to administrative precedent. (Apparently, there were no further circumstances urged by Theodoropoulos as bases for finding jurisdiction.) Contrary to the dissent’s characterization, we did not hold in Theodoropoulos II that “(absent a Constitutional problem) there is no exception to the exhaustion requirement for any claim that could have been raised in the BIA,” see post (emphasis added). We specifically limited the holding of Theodoro-poulos II to the facts by declining to fix the “precise boundaries” of possible exceptions to the exhaustion rule. 358 F.3d at 173. Marrero Pichardo simply adds further definition to these boundaries in analyzing the facts of that case.
Finally, we have the power to consider the legal incoherence of Gill’s crime of conviction even though Gill has not raised it here. See Lambert v. Genesee Hosp., 10 F.3d 46, 56 (2d Cir.1993) (“[W]e have discretion to consider and decide sua sponte a dispositive issue of law.”), cert. denied, 511 U.S. 1052, 114 S.Ct. 1612, 128 L.Ed.2d 339 (1994); see also Thomas v. Crosby, 371 F.3d 782, 793 (11th Cir.2004) (Tjoflat, J. concurring) (“It is beyond dispute that, in general, we have the power to consider issues that a party fails to raise on appeal, even though the petitioner does not have the right to demand such consideration.”); United States v. Boyd, 208 F.3d 638, 652 (7th Cir.2000) (finding an inter-circuit consensus that courts of appeals “may, when justice requires it, raise critical issues of law sua sponte”), vacated on other grounds, 531 U.S. 1135, 121 S.Ct. 1072, 148 L.Ed.2d 949 (2001); Cruz v. Me-[89]*89lecio, 204 F.3d 14, 22 n. 7 (1st Cir.2000) (“Notwithstanding that the parties did not raise the issues that impel us to this course either to the district court or on this appeal, we have the power to do so sua sponte.”); United States v. Heater, 63 F.3d 311, 331 n. 5 (4th Cir.1995) (“Although [petitioner] did not raise the Ex Post Facto argument himself, we find it within our discretion to consider this constitutional concern sua sponte.”), cert. denied, 516 U.S. 1083, 116 S.Ct. 796, 133 L.Ed.2d 744 (1996).
II. Standard of Review
Because the BIA has expertise applying and construing immigration law, we afford Chew'on deference to its construction of undefined statutory terms such as “moral turpitude.” See Chevron U.S.A., Inc. v. Natural Res. Def. Council, Inc., 467 U.S. 837, 843-44, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984); Michel v. INS, 206 F.3d 253, 262-65 (2d Cir.2000) (deferring to BIA’s rule that crimes of which knowledge is an element are generally CIMTs). However, as we recognized in Michel, 206 F.3d at 262, the BIA has no expertise in construing federal and state criminal statutes, and so we review de novo the BIA’s finding that a petitioner’s crime of conviction contains those elements which have been properly found to constitute a CIMT. See also Sutherland v. Reno, 228 F.3d 171, 174 (2d Cir.2000). Thus, in this case, we defer to the BIA’s view that recklessness, in combination with serious resulting bodily injury and use of a deadly weapon, amounts to a CIMT, but we review de novo the BIA’s finding that “attempted reckless assault” under New York law contains these elements.
III. Gill’s alleged CIMT
We turn now to the question of whether Gill’s conviction for attempted reckless assault was a CIMT such that he was removable under 8 U.S.C. § 1227(a)(2)(A)(i).
A. Definition of CIMT in immigration law
At the outset, we affirm the BIA’s holding that reckless assault with a deadly instrument resulting in serious bodily harm is a CIMT. “Moral turpitude” is a term used to refer to offenses that are “inherently base, vile, or depraved.” Hamdan v. INS, 98 F.3d 183, 186 (5th Cir.1996) (quoting from the BIA decision). In assessing whether a crime of conviction is a CIMT, the BIA takes the “categorical approach,” focusing on “the intrinsic nature of the offense rather than on the factual circumstances surrounding any particular violation.” Dalton v. Ashcroft, 257 F.3d 200, 204 (2d Cir.2001). Thus, to constitute a CIMT, a criminal category must by definition, and in all instances, contain each of those elements that constitute a CIMT. Michel, 206 F.3d at 263.
“[I]t is in the intent that moral turpitude inheres,” United States ex rel. Meyer v. Day, 54 F.2d 336, 337 (2d Cir.1931), and therefore the BIA’s focus is on the mental state reflected in a given offense. Crimes committed knowingly or intentionally generally have been found, on the categorical approach, to be CIMTs. Michel, 206 F.3d at 263. Likewise, crimes committed recklessly (where recklessness is defined as a conscious disregard of substantial and unjustifiable risk) have, in certain aggravated circumstances, been found to express a sufficiently corrupt mental state to constitute a CIMT. See, e.g., Matter of Medina, 15 I. & N. Dec. 611, 614 (BIA 1976) (holding that, although moral turpitude does not inhere in all crimes of recklessness, it does inhere in reckless assault with a deadly weapon); cf. Matter of Fualaau, 21 I. & N. Dec. 475, 478 (BIA 1996) (holding that [90]*90reckless assault was not a CIMT because no serious bodily injury resulted).
We find that the BIA’s definition of “moral turpitude” is consistent with the precedent set forth supra, and is reasonable.
B. Gill’s crime of conviction
As set forth supra, we now review de novo the BIA’s characterization of Gill’s crime of conviction. Gill pleaded guilty to attempted second-degree assault in violation of N.Y.P.L. § 120.05(4)-that is, attempting to “recklessly cause[] serious physical injury to another person by means of a deadly weapon or a dangerous instrument.” Under New York law, “[a] person is guilty of an attempt to commit a crime when, with intent to commit a crime, he engages in conduct which tends to effect the commission of such crime.” N.Y.P.L. § 110.00. This standard has been characterized as a specific intent standard. People v. Campbell, 72 N.Y.2d 602, 605, 535 N.Y.S.2d 580, 581-82, 532 N.E.2d 86, 87-88 (1988).
A charge of attempting to commit a crime of recklessness has a certain conceptual incoherence, particularly where, as here, the offense is partly defined by its result (serious bodily injury). A defendant can only be guilty of attempted assault if he specifically intended all elements of that offense, but § 120.05(4) is worded such that a defendant can be convicted simply because his assault resulted in serious injury, regardless of whether he intended such a result. Recognizing this type of incoherence, the New York Court of Appeals dismissed an analogous charge in Campbell, 72 N.Y.2d at 605, 535 N.Y.S.2d at 582, 532 N.E.2d at 88.11 The court reasoned that, “[bjecause the very essence of a criminal attempt is the defendant’s intention to cause the proscribed result, it follows that there can be no attempt to commit a crime which makes the causing of a certain result criminal even though wholly unintended,” and thus “there can be no attempt to commit assault, second degree (Penal Law § 120.05[3]).”
In People v. Esquilin, 159 A.D.2d 632, 633, 552 N.Y.S.2d 953, 955 (2d Dep’t 1990), the Appellate Division extended Campbell’s holding to reverse a jury conviction for attempted kidnapping. There, the court held that, like second degree assault,
kidnapping in the first degree under Penal Law § 135.25(3) occurs when the accused, with intent to restrain the victim, does so restrain the victim by the use or threatened use of deadly force and, during the course of this abduction the victim dies. The gravamen of this charge is not the abduction but, rather, the unintended death. The causing of this result being criminal even if unintended, it follows that there can be no attempt to cause this result.
Id. (citations omitted).
The legal incoherence theory has also been applied to crimes of recklessness. In People v. Terry, 104 A.D.2d 572, 573, 479 N.Y.S.2d 278, 279-80 (2d Dep’t 1984), for example, the Appellate Division reversed a jury conviction of attempted second degree murder, holding that one cannot attempt to commit second degree murder, ie., cause someone’s death by “recklessly engaging] in conduct which creates a grave risk of death to another person,” under circumstances “evincing a depraved indifference to human life.” N.Y.P.L. [91]*91§ 125.25(2). Because § 125.25(2) “involves no intent, only a culpable mental state of recklessness,” the court explained, it is incompatible with the specific intent requirement of the criminal attempt provision. Terry, 104 A.D.2d at 573, 479 N.Y.S.2d at 279-80; see also People v. McDavis, 97 A.D.2d 302, 303, 469 N.Y.S.2d 508, 510 (4th Dep’t 1983) (“[T]here can be no attempt to commit a crime that does not involve a specific intent, such as manslaughter in the second degree, a crime predicated upon a reckless act.”); People v. Trepanier, 84 A.D.2d 374, 380, 446 N.Y.S.2d 829, 833 (4th Dep’t 1982) (“The crime of attempted reckless endangerment is nonexistent since it is a non-intent offense.”)
As these cases demonstrate, a person cannot “attempt” (as this term is used in New York criminal law) to commit a crime of recklessness, particularly not one defined, as in § 120.05(4), by an unintended result such as bodily injury. The question that follows is what significance, if any, this legal impossibility should have in the immigration context. Although this is a question of first impression in this circuit as well as in most other circuits, the Third Circuit addressed the question in a case interpreting New York law: Knapik v. Ashcroft, 384 F.3d 84 (3d Cir.2004). In that case, the court considered a BIA determination that Knapik’s crime of conviction-attempted reckless endangerment-was a CIMT. The Knapik court found that the concept of intentional recklessness was “nonsensical,” and that New York courts had recognized it as such. Id. at 91 (citing Terry, 104 A.D.2d 572, 479 N.Y.S.2d 278; Trepanier, 84 A.D.2d 374, 446 N.Y.S.2d 829). Because Knapik’s crime of conviction was nonsensical, the court found that it could not demonstrate “moral turpitude.”
We find the Third Circuit’s logic persuasive and directly on point. Without in any way questioning the state’s ability to hold a defendant to his plea to an attempted reckless crime (which may have made practical sense in terms of reaching a contextually appropriate sentence or sentencing range),12 we find that, in the immigration context, no mental state can be clearly discerned from such a conviction, let alone the sort of aggravated recklessness that has been found to demonstrate moral turpitude, see Matter of Medina, 15 I. & N. Dec. 611, 613-14 (BIA 1976).
CONCLUSION
For the foregoing reasons, because Gill’s crime of conviction was not a crime involving moral turpitude, we reverse the BIA’s removal order and remand with instructions to close Gill’s removal proceedings. The stay of removal, which was in place pending our decision, will expire upon issuance of the mandate.