BOUDIN, Circuit Judge.

Fitzroy Delgado Campbell seeks review of a Board of Immigration Appeals ("BIA") decision ordering his removal. Campbell, a lawful permanent resident of the United States, was arrested in June 2006 and charged under Connecticut law with two counts of sexual assault in the fourth degree as well as two counts of risk of injury to a minor. In a plea bargain, both sexual assault charges and one of the two risk-of-injury counts were dismissed, and Campbell entered a plea of nolo contendere to one count of risk of injury to a minor under section 53-21(a)(1) of the Connecticut General Statutes.

That statute (the emphasis is ours) reads as follows:

Conn. Gen.Stat. Ann. § 53-21(a)(1) (West 2006).

The maximum sentence for a violation of section 53-21(a)(1) is ten years imprisonment plus a $500 fine. Act of May 30, 1995, Conn. Pub. Act. No. 95-142, § 1, 1995 Conn. Legis. Serv. P.A. 95-142 (West). Following the plea agreement and as contemplated, the judge sentenced Campbell to five years in prison with the sentence fully suspended, and five years of probation. Among the conditions of the probation, the judge ordered Campbell to undergo sex offender evaluation and treatment, to have no contact with the child whom he was charged with endangering, and to have no unsupervised contact with any minor children under sixteen.

On November 2, 2010, the Department of Homeland Security ("DHS") began removal proceedings under the Immigration and Nationality Act ("INA") § 240, 8 U.S.C. § 1229a (2006). The notice asserted that Campbell was removable on three separate grounds:

The latter two offense categories — "crime of violence" and "murder, rape, or sexual abuse of a minor" — qualify as aggravated felonies under the INA, and a permanent resident who is convicted of an aggravated felony is not only subject to removal but ineligible for cancellation of removal. INA § 240A(b)(1)(C), 8 U.S.C. § 1229b(b)(1)(C); Emile v. INS, 244 F.3d 183, 184-85 (1st Cir.2001). By contrast, "[a]liens who have committed child abuse [as opposed to sexual abuse of a minor] are not considered aggravated felons and are eligible for cancellation of removal" at the discretion of the Attorney General. Guerrero-Perez v. INS, 242 F.3d 727, 728 (7th Cir.2001).

Campbell, represented by counsel, appeared before an immigration judge ("IJ") in Boston on May 26, 2011. In an oral decision, the IJ ruled that Campbell was removable on all three of the grounds asserted by DHS — child abuse, crime of violence, and sexual abuse of a minor — and that as an aggravated felon, Campbell was ineligible for cancellation of removal. In so concluding, the IJ relied on the facts asserted by the prosecution in the February 2007 plea colloquy as well as "the record as a whole."

Campbell sought review by the BIA, which affirmed the IJ's ruling on October 31, 2011. The BIA addressed only the government's argument that Campbell had been convicted of sexual abuse of a minor; it did not address the government's arguments with respect to the child-abuse and crime-of-violence grounds for removal. Campbell then petitioned this court for review. INA § 242(b)(1), 8 U.S.C. § 1252(b)(1). Although Campbell was removed to Jamaica after this court denied a motion for a stay, his appeal remains viable. Nken v. Holder, 556 U.S. 418, 424, 129 S.Ct. 1749, 173 L.Ed.2d 550 (2009).

Where the government asserts that a non-citizen has been convicted of a crime rendering him removable, the government must so prove by "clear and convincing evidence." Conteh v. Gonzales, 461 F.3d 45, 52 (1st Cir.2006), cert. denied, 551 U.S. 1148, 127 S.Ct. 3003, 168 L.Ed.2d 732 (2007); see also INA § 240(c)(3)(A), 8 U.S.C. § 1229a(c)(3)(A). Whether the offense for which the non-citizen was convicted constitutes a ground for removal — or, in dispute here, an "aggravated felony" precluding cancellation of removal — is a legal issue subject to de novo review by this court. Ramirez v. Mukasey, 520 F.3d 47, 48 (1st Cir.2008); Conteh, 461 F.3d at 52.

The fourth degree sexual assault charges against Campbell, Conn. Gen.Stat. § 53a-73a (West 2006), were dismissed, so our concern is solely with the endangerment offense limned in section 53-21(a)(1) to which Campbell pled nolo contendere. Both language and precedent confirm that that statute can be violated by conduct wholly different than sexual assault. The plain language of section 53-21(a)(1) would suggest that any serious willful endangerment of a child's life, limb, health or morals is criminal under the statute, and Connecticut case law confirms this reading.1

One unfamiliar with federal precedent might assume that the next question would be whether Campbell's actual conduct pertaining to the offense comprised "sexual abuse" as that term is used in the INA; but a quite different set of questions are posed by governing case law both for the removal provisions and for analogous provisions which may enhance sentences in the federal criminal context based on prior specified convictions — in particular the Armed Career Criminal Act ("ACCA"), 18 U.S.C. § 924(e), and the career offender guideline, U.S.S.G. § 4B1.2.

When a state or federal statute of conviction encompasses some conduct that would qualify as a predicate offense under the ACCA or career offender guideline and some conduct that would not, governing Supreme Court precedent — as this and most other circuits understand it — requires that we answer two questions:

Taylor v. United States, 495 U.S. 575, 110 S.Ct. 2143, 109 L.Ed.2d 607 (1990), and Shepard v. United States, 544 U.S. 13, 125 S.Ct. 1254, 161 L.Ed.2d 205 (2005), established this methodology in the criminal context based in part on statutory language, arguably similar in the federal criminal context and in the immigration statute,2 as well as on "practical difficulties and potential unfairness" that would arise from determining underlying conduct. Taylor, 495 U.S. at 600-02, 110 S.Ct. 2143. The second step in the Taylor-Shepard framework is sometimes called "the modified categorical approach," although that phrase has sometimes been used for other purposes. Conteh, 461 F.3d at 55.

The Taylor-Shepard approach is widely taken to mean that the court should look to the crime of conviction, that is, the elements of the statute or common law offense. Moreover, under Taylor-Shepard, the facts underlying the conviction are relevant, if at all, only to identify which crime is the crime of conviction where (as is often true with divisible statutes) it is unclear which subsumed offense the defendant pled to or was found to have violated. To this limited extent, Shepard can be seen as modifying Taylor's emphasis on convictions as opposed to underlying facts.

In its 2010 decision in Johnson v. United States, ___ U.S. ___, 130 S.Ct. 1265, 176 L.Ed.2d 1 (2010), seeking to determine whether a defendant's conviction for simple battery under Florida law was a "violent felony" for purposes of the ACCA, the Supreme Court explained:

Id. at 1273 (quoting Nijhawan v. Holder, 557 U.S. 29, 41, 129 S.Ct. 2294, 174 L.Ed.2d 22 (2009)) (citation omitted).

Johnson makes clear that while a criminal statute may be divisible into several generic crimes — by explicit subdivisions, "or" conjunctions, or definitive glosses — one of those subordinate offenses must express or equate to the critical concept (in Johnson, "violent force"); otherwise a conviction under the statute is irrelevant and sources like the plea colloquy ought not be consulted. United States v. Beardsley, 691 F.3d 252, 263, 270 (2d Cir. 2012); United States v. Del Carmen Gomez, 690 F.3d 194, 198-99 (4th Cir.2012).

Although the BIA has said that the Taylor-Shepard approach "need not be applied with the same rigor in the immigration context as in the criminal arena," In re Lanferman, 25 I. & N. Dec. 721, 727-28 (B.I.A.2012), the Supreme Court's decision in Nijhawan v. Holder, 557 U.S. 29, 129 S.Ct. 2294, 174 L.Ed.2d 22 (2009), requires the Taylor-Shepard analysis in INA cases — save where the matching INA offense is phrased so as to require a fact-specific determination rather than identification of a generic crime.3 Further, certain offenses listed in INA § 101(a)(43) "must refer to generic crimes" and one such offense is "sexual abuse of a minor." Nijhawan, 557 U.S. at 37, 129 S.Ct. 2294; accord Sanchez-Avalos v. Holder, 693 F.3d 1011, 1015 n. 1 (9th Cir.2012).

More recently the Supreme Court again stressed that (fact-specific provisions aside), the categorical approach operates similarly in the INA context as in the criminal context. In Kawashima v. Holder, ___ U.S. ___, 132 S.Ct. 1166, 182 L.Ed.2d 1 (2012), the Court said: "To determine whether the Kawashimas' offenses `involv[e] fraud or deceit' within the meaning of [the INA aggravated felony statute], we employ a categorical approach by looking to the statute defining the crime of conviction, rather than to the specific facts underlying the crime." Id. at 1172.

Taylor-Shepard's focus on the statute rather than the conduct disturbs some courts;4 and, until recently, the Supreme Court's guidance as to INA cases was not crystal clear. Thus in Conteh, decided three years before Nijhawan, this court held that facts showing the amount of loss could be used to determine whether a non-citizen had been convicted of an offense involving "fraud or deceit in which the loss to the ... victims exceeds $10,000" (an aggravated felony), even though the non-citizen was convicted under a statute with no loss element. Conteh, 461 F.3d at 52-57; cf. INA § 101(a)(43)(M)(i), 8 U.S.C. § 1101(a)(43)(M)(i).

But we also said in Conteh that "[w]e need go no further" to resolve that case, Conteh, 461 F.3d at 65, and we emphasized that as a general rule, "the BIA may not adjudicate guilt" and "must base removal orders on convictions, not on conduct alone." Conteh, 461 F.3d at 56. The Supreme Court in Nijhawan endorsed Conteh's exception as to INA provisions phrased in fact-specific terms such as the amount-of-loss clause in INA § 101(a)(43)(M)(i), but it set a limit by continuing to exclude fact-specific inquiries for generically phrased provisions that were not divisible into subordinate offenses.

Because of the vagaries of statute drafting, the Taylor-Shepard methodology has proved far more difficult to apply than the Supreme Court may have anticipated.5 But the Supreme Court has shown no inclination to alter it in the criminal context, Johnson, 130 S.Ct. at 1273-74, or, with the modest exception adopted in Nijhawan, for immigration cases. Every solution to the riddle of determining the "crime of conviction" in cases of broadly-defined offenses poses problems, and at least the most recent Supreme Court decisions may have furnished stability to the terms of the inquiry.

On this understanding, we turn to the Connecticut statute. If section 53-21(a)(1) were read as prescribing a single "offense," the offense so described would (as already noted) include conduct having nothing to do with sexual abuse and thus would not disqualify Campbell from cancellation of removal. Alternatively, section 53-21(a)(1) could fairly be read as divisible, by virtue of the "or" clauses, in which event the two most pertinent offenses would be endangering "the health" of a child and endangering a child's "morals."

Yet, a child's health could be endangered in other ways than sexual abuse — for example, letting a child play with a loaded gun6 — and a child's "morals" could likewise be impaired through nonsexual conduct: Imagine Fagin indoctrinating Oliver Twist into a life of crime. So each of the arguably relevant separate offenses fails to define crimes that categorically correspond to or require sexual abuse for their commission. It is hard to see how the statute could be further divided except by making determinative actual conduct rather than the crime of conviction.

This might be a different case had the Connecticut courts by construction limited the morals clause solely to serious sexual abuse — surely impossible for the health clause — and decisions of the state's highest court might hint at such a reading, cf. State v. Schriver, 207 Conn. 456, 542 A.2d 686 (1988); State v. Robert H., 273 Conn. 56, 866 A.2d 1255 (2005). But the government has not so argued and anyway that would over-read those cases. Cf. Bourguignon v. Warden-Cheshire, No. CV020469954S, 2005 WL 1759747, at *4-5, 2005 Conn.Super. LEXIS 1626, at *12-14 (Conn.Super.Ct. June 22, 2005) (indicating that conduct that does not involve a sexual act, such as giving alcohol to a child, may qualify as impairment of health or morals).

Taylor-Shepard often entails a gap between the "offense" and the actual conduct, and generally makes the former decisive. Sometimes this hurts the alien or criminal defendant — for example, a conviction under a state burglary statute can qualify as a categorical "violent felony" under the ACCA even though the defendant's actual conduct may have involved a "break-in of an unoccupied structure located far off the beaten path" where no violence could or did occur. See, e.g., James v. United States, 550 U.S. 192, 207-08, 127 S.Ct. 1586, 167 L.Ed.2d 532 (2007). Other times, as in this case, the alien or defendant comes out ahead. This is hardly the most jarring example.7

While the criminal information in Campbell's case identified no specific conduct, the prosecutor in describing the charges she would try to prove identified two sexual touchings, and the trial court required sex offender evaluation and treatment (although not sex offender registration). But the court assured Campbell twice that he was admitting to no conduct whatsoever and the judge himself made no findings as to the underlying conduct. In any event, the facts in the record of conviction do not alter the outcome here.

Our decision today settles only that Campbell cannot be held to have pled to an offense that falls within the sexual abuse rubric under the INA. The Board did not rule on whether Campbell would be removable on the alternative grounds of child abuse (which would leave him eligible for cancellation of removal) or on the grounds that he was convicted of a "crime of violence" (which would render him ineligible for cancellation), and since the Board did not reach these issues, neither do we. See INS v. Ventura, 537 U.S. 12, 17, 123 S.Ct. 353, 154 L.Ed.2d 272 (2002).

The Board's ruling is reversed insofar as it holds that Campbell is removable on the grounds that he was convicted of aggravated felony sexual abuse and that he is therefore ineligible for cancellation of removal; its order dismissing his appeal is vacated and the matter is remanded to the Board for further proceedings consistent with this decision.

It is so ordered.