ORDER

Three years ago, a bevy of police officers, acting on an informant’s tip, raided a Milwaukee home 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 Brewer’s car, which was parked in front of the residence. A grand jury returned a superseding indictment charging Brewer with possession of 50 grams or more of crack cocaine with intent to distribute, 21 U.S.C. § 841(a)(1), (b)(l)(A)(iii), and of possession of a firearm by a felon, 18 U.S.C. § 922(g)(1). At his bench trial, Brewer stipulated to all of the facts necessary to establish that he possessed the firearm 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 reaching its decision, the court noted that the evidence clearly established that Brewer possessed cocaine base (police discovered 8.556 grams of the drug in his mouth) but nevertheless acquitted him under § 841(a)(1) because the court could not find, beyond a reasonable doubt, that Brewer intended to distribute the crack.

After the district court announced its verdicts, the government asked the court to convict Brewer of simple possession of cocaine base under 21 U.S.C. § 844(a) because, in the government’s view, it was 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.” The court accepted the government’s request and found Brewer guilty of possessing more than 5 grams of cocaine base under § 844(a). He was sentenced to two concurrent terms of 110 months. Brewer appeals.

In United States v. Hill, 196 F.3d 806 (7th Cir. 1999), 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. Brewer, however, 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). Because Brewer was convicted on a possession charge that had an additional element— that the drug be “cocaine base” — the district court erred in finding him guilty as it did under the third sentence of § 844(a). The only appropriate lesser-included offense of the drug charge alleged in Brewer’s indictment is simple possession under the first sentence of § 844(a), and so, under 28 U.S.C. § 2106, we vacate his drug conviction and remand the case to the district court with directions to enter a judgment on the true lesser-included offense.

*925In remanding this case, we note that the record is unclear regarding how Brewer’s erroneous drug conviction affected his 110-month sentence on the firearm charge. If Brewer were convicted of the true lesser-included offense, any grouping of offenses would not be allowed under U.S.S.G. § 3D1.2. Any calculation of the combined offense level would also have been tainted by either (1) the court’s inability to group, or (2) Brewer’s improperly inflated base offense under the erroneous drug conviction. This problem is exacerbated by the fact that it is not clear whether the court imposed any increases for specific offense characteristics. Therefore, at this time, based on this record, we voice no opinion regarding the continued validity of the sentence Brewer received on the firearm charge. That will be a matter for the district court to consider upon remand.

REVERSED and REMANDED.