The Paulus defense, requiring a controlled substances offense to involve a federally-listed controlled substance, may have some limitations. See Martinez-Espinoza, 25 I&N Dec. 118, 121 (BIA 2009) ("Second, we have long drawn a distinction between crimes involving the possession or distribution of a particular drug and those involving other conduct associated with the drug trade in general. Thus, the requirement of a correspondence between the Federal and State controlled substance schedules, embraced by Matter of Paulus, 11 I&N Dec. 274, for cases involving the possession of particular substances, has never been extended to other contexts by the Board. For example, in Matter of Martinez-Gomez, 14 I&N Dec. 104, 105 (BIA 1972), we held that an aliens California conviction for opening or maintaining a place for the purpose of unlawfully
selling, giving away, or using any narcotic was a violation of a law relating to illicit traffic in narcotic drugs under former section 241(a)(11) of the Act, 8 U.S.C. 1251(a)(11) (1970), even though the California statute required no showing that only Federal narcotic drugs were sold or used in the place maintained, because the primary purpose of the law was to eliminate or control traffic in narcotics). In addition, the BIA stated:

First, in Paulus and Ruiz-Vidal the Government bore the burden of proving that an alien was deportable because of a controlled substance violation. But here the sole question is whether the respondent can meet his burden of proving eligibility for adjustment of status. Section 291 of the Act, 8 U.S.C. 1361 (2006); see also Matter of Rainford, 20 I&N Dec. 598, 599 (BIA 1992) (The burden of proving eligibility for the privilege of adjustment of status is upon the alien.). Under the regulations, moreover, [i]f the evidence indicates that one or more of the grounds for mandatory denial of the application for relief may apply, the alien shall have the burden of proving by a preponderance of the evidence that such grounds do not apply. 8 C.F.R. 1240.8(d) (2009). Inadmissibility to the United States is a ground for mandatory denial of adjustment of status, and the respondents drug paraphernalia conviction raises a legitimate question as to whether that ground for mandatory denial may apply in his case. Id. Thus, the respondent bears the burden to resolve any issue that might arise in his case by virtue of an asymmetry between the Federal and State controlled substance schedules.

(Id. at 121.)

In Matter of Hernandez-Ponce, 19 I.& N. Dec. 613 (BIA 1988), the Board said being under the influence became a deportable conviction relating to a controlled substance after the ADAA Act passed in 1988, but it seemed to include the fact that Phencyclidine is listed as a controlled substance in the CSA, as a key fact underpinning the ruling:

The Service, in its written brief, asserts that, by enacting the Anti-Drug Abuse Act, Congress the deportation statute now renders deportable any alien convicted of any law relating to controlled substances, including being `under the influence of a controlled substance.

It is evident to us, according to the plain words of the amended statute, that Congress intended to expand rather than limit the power of the Government to curtail drug abuse through the immigration laws. Prior to the recent amendments, section 241(a)(11) listed the specific drug-related criminal activities which Congress considered sufficient to warrant the exclusion or deportation of aliens. The amended statute refers to `any law or regulation relating to a controlled substance. These are words which, according to our construction, clearly contain no limitation. Thus, our construction of the former statute set forth in Matter of Sum, supra, which distinguished a conviction for unlawful use of a proscribed drug from a conviction for its unlawful possession, was based on the clearly different language of the former statute and is clearly incompatible with the plain meaning of the amended statute.

In the case before us, the respondent has admitted to being twice convicted for the crime of use and being under the influence of phencyclidine. Phencyclidine is listed as a controlled substance under the Controlled Substances Act. We must conclude that the respondent falls within the purview of the amended language of section 241(a)(11) of the Act, which refers to convictions `relating to a controlled substance.` Accordingly, the decision of the immigration judge relating to the respondent's deportability will be affirmed.

(Id. at 616.) Thanks to Jonathan Moore.