With a narrowband multiuser detector (MUD), multiple users can simultaneously share the same channel without using a bandwidth-expanding signature code when sufficient power differences at the receiver are maintained. In this paper, we assess the capacity gain that can be achieved in a hypothetical cellular system with centralized power control, using a narrowband MUD based on successive cancellation. The power-control algorithm is adapted to multiple users per channel in a cell. Simulation results are presented for two heuristic carrier-to-interference ratio-based channel-assignment schemes. The MUD allows for a substantial capacity gain due to a tighter packing of users in a channel. The observed gain compared with a conventional single user-per-channel system, ranges from 1.4 to 5 for cluster sizes C = 1 and 7, respectively.