ORDER
Previously in this direct criminal appeal, we denied a motion to withdraw filed by appointed counsel David J. Lang because in his supporting brief he mischaracterized as frivolous a potential issue for appeal. See Anders v. California, 386 U.S. 738, 87 S.Ct. 1396, 18 L.Ed.2d 493 (1967). And although we ordered briefing on the merits, Mr. Lang has again moved to withdraw, iterating that there are no nonfrivolous issues for appeal. We disagree and will appoint another lawyer to represent the appellant.
On May 9, 2000, police acting on an informant’s tip raided a home in Milwaukee, Wisconsin, and discovered large quantities of drugs and drug paraphernalia. Curtis Brewer, who had been convicted of distributing cocaine base in 1993, was apprehended as he tried to flee the home. Police later discovered a firearm in Mr. Brewer’s car, which was parked in front of the residence. A grand jury returned a superceding indictment charging Mr. Brewer with possession of 50 grams or more of crack cocaine with intent to distribute, 21 U.S.C. § 841(a)(1), (b)(1)(A)(iii), and of possession of a firearm by a felon, 18 U.S.C. § 922(g)(1). At his bench trial Mr. Brewer stipulated to all of the facts necessary to establish that he possessed a gun in violation of § 922(g)(1), but he contested the drug charge. The district court eventually found him guilty of the gun charge but not guilty of possession with intent to distribute under § 841(a)(1). In rendering its verdicts, the court noted that the evidence clearly established that Mr. Brewer possessed cocaine base (police discovered 8.556 grams of the drug in his mouth), but nevertheless acquitted him under § 841(a)(1) because there was reasonable doubt as to whether he intended to distribute it.
*320After the district court announced its verdicts, the government requested that the court convict Mr. Brewer of simple possession of cocaine base under 21 U.S.C. § 844(a) because, in the government’s view, that offense is a lesser-included offense of possession of a controlled substance with intent to distribute under § 841(a)(1). The government made this request pursuant to Federal Rule of Criminal Procedure 31(c), which authorizes conviction on any “offense necessarily included in the offense charged.” After taking the government’s request under advisement, the court found Mr. Brewer guilty of possessing more than five grams of cocaine base under § 844(a). The court then sentenced him to two concurrent terms of 110 months’ incarceration and two concurrent terms of three years’ supervised release.
In his original Anders brief, counsel, citing United States v. Hill, 196 F.3d 806, 808 (7th Cir.1999), concluded that it would be frivolous for Mr. Brewer to argue that he was improperly convicted of possessing more than five grams of cocaine base under § 844(a) because, according to counsel, that offense is a lesser-included offense of possession of a controlled substance with intent to distribute under § 841(a)(1). In Hill we recognized that simple possession of a controlled substance is a lesser-included offense of possession with intent to distribute because “simple possession is possession with intent to distribute minus intent to distribute.” Hill, 196 F.3d at 808. But Mr. Brewer was convicted of possession of cocaine base, and Hill, citing United States v. Michael, 10 F.3d 838 (D.C.Cir.1993), acknowledged that § 844(a) creates a separate crime of possession of cocaine base that is not a lesser-included offense of possession with intent to distribute a controlled substance under § 841(a)(1). See Hill, 196 F.3d at 808; see also United States v. Steward, 252 F.3d 908, 909 (7th Cir.2001). Thus, in denying counsel’s motion we identified two questions: (1) whether the district court, acting under Rule 31(c), erred by finding Mr. Brewer guilty of possessing more than five grams of crack cocaine under § 844(a) as a lesser-included offense of the charged offense of possession of a controlled substance with intent to distribute under § 841(a)(1); and (2) whether this court may direct the district court under 28 U.S.C. § 2106 to enter a judgment of conviction on the lesser-included offense of simple possession of a controlled substance under § 844(a).
Counsel now contends that the district court did indeed err by convicting Mr. Brewer of possessing more than five grams of crack cocaine under § 844(a) as a lesser-included offense of the charged offense of possession of a controlled substance with intent to distribute under § 841(a)(1). But counsel nevertheless concludes that any potential appeal would be frivolous because, in his view, the district court’s error was harmless. According to counsel, this court may direct the district court to enter a judgment of conviction on the true lesser-included offense-simple possession of a controlled substance under § 844(a). See 28 U.S.C. § 2106. Counsel further contends, however, that remanding the case would be unnecessary because, in his view, “the sentence given to Curtis Brewer by Judge Clevert would be the same and have the same effect.” But counsel does not explain how or why Mr. Brewer’s sentences would be the same. Because the court convicted Mr. Brewer of possessing more than five grams cocaine base, it utilized the cross-referencing section of U.S.S.G. § 2D2.1 to determine his offense level for the drug offense. The court also imposed a two-level multi-count upward adjustment under U.S.S.G. § 3D 1.4 because he was also convicted of unlawful firearm possession. But if Mr. *321Brewer were to be convicted of simple possession of a controlled substance under § 844(a), neither of these provisions would apply.
Mr. Lang has failed twice to advance potentially nonfrivolous arguments on Mr. Brewer’s behalf. Accordingly, IT IS ORDERED that the motion to withdraw is GRANTED, and attorney David J. Lang is discharged. Another lawyer will be appointed for Mr. Brewer by separate order, and the clerk of this court is directed to furnish new counsel with a copy of this order. New counsel should brief the “lesser-included offense” and § 2106 issues, as well as any other issue counsel deems appropriate.