this violence, will not tolerate people who have such a record from committing other crimes. I am required to impose this sentence given the legal framework under which we operate. It is a just sentence.
A.
The Eighth Amendment
Cardoza supports his Eighth Amendment challenge on the basis of the Supreme Court’s decision in Solem v. Helm, 463 U.S. 277, 103 S.Ct. 3001, 77 L.Ed.2d 637 (1983), arguing that his sentence, like the life sentence imposed in Helm under a recidivist statute for writing a $100 “no-account” check, is “significantly disproportionate to his crime, and is therefore prohibited by the Eighth Amendment,” id. at 303, 103 S.Ct. at 3016-17. He acknowledges that we have rejected a facial challenge to the constitutionality of the ACCA, United States v. Gilliard, 847 F.2d 21, 27 (1st Cir.1988), and instead questions only the constitutionality of the ACCA provisions as applied to him, given that his possessory offense involved only one bullet.
Although the Court in Helm stated that “[t]he constitutional principle of proportionality has been recognized explicitly in the Court for almost a century,” Helm, 463 U.S. at 286, 103 S.Ct. at 3007-08, it also recognized that “prior convictions are relevant to the sentencing decision”, id. at 296 n. 21, 103 S.Ct. at 3013 n. 21. Similarly, the Court’s most recent examination of proportionality has, at the very least, cast doubt on the exact method by which a reviewing court should approach such challenges in non-capital cases. In the plurality opinion of Harmelin v. Michigan, 501 U.S. 957, 111 S.Ct. 2680, 115 L.Ed.2d 836 (1991), two justices sought to limit proportionality review to capital cases only, id. at 994, 111 S.Ct. at 2701 (opinion of Scalia, J., joined by Rehnquist, C.J.), three justices recognized a “narrow proportionality principle,” id. at 997, 111 S.Ct. at 2702 (opinion of Kennedy, J., joined by O’Connor and Souter, JJ.), and three justices dissented on the grounds that Helm’s three-factor proportionality review controlled, id. at 1021, 111 S.Ct. at 2715-16 (White, J., dissenting, joined by Blackmun and Stevens, JJ.). We have interpreted Harmelin to require a defendant seeking proportionality review to demonstrate, at the threshold, an “initial inference of gross dis-proportionality,” Tart v. Commonwealth of Massachusetts, 949 F.2d 490, 503 n. 16 (1st Cir.1991), between the “gravity of [the] criminal conduct and the severity of the ... penalty” imposed, United States v. Bucuvalas, 970 F.2d 937, 946 (1st Cir.1992). See Harmelin, 501 U.S. at 1005, 111 S.Ct. at 2707 (opinion of Kennedy, J.) (“[I]ntrajurisdictional and interjurisdictional analyses are appropriate only in the rare case in which a threshold comparison of the crime committed and the sentence imposed leads to an inference of gross disproportionality.”); United States v. Graciani, 61 F.3d 70, 76 (1st Cir.1995); United States v. Saccoccia, 58 F.3d 754, 788-89 (1st Cir.1995), cert. denied, — U.S. —, 116 S.Ct. 1322, 134 L.Ed.2d 474 (1996).
Thus, in Graciani we upheld a 280-month sentence for the distribution of 85.3 grams of crack cocaine against a proportionality attack. 61 F.3d at 73, 77. Similarly, in Sac-coccia we upheld a mandatory life sentence in a drug-money laundering scheme, stating that
Congress — not the judiciary — is vested with the authority to define,, and attempt to solve, the societal problems created by drug trafficking across national and state borders. The Supreme Court has made it plain that the use of severe penalties as part of the legislative armamentarium does not constitute cruel and unusual punishment.
58 F.3d at 789.
Against this backdrop, we cannot say that Cardoza’s sentence supports the necessary “inference of gross disproportionality.” Bucuvalas, 970 F.2d at 946. Cardoza has not been sentenced to a 235-month incarceration solely because he was in possession of a single bullet, as his brief strenuously argues. Rather, he has been sentenced to such a term because (1) he was a convicted felon in possession of the bullet, and (2) he had previously been convicted of at least three violent felonies. Further, despite counsel for appellant’s position at oral argument, a bullet is