A polishing apparatus includes a plurality of stations supported on a platform, the plurality of stations including at least two polishing stations and a transfer station, each polishing station including a platen to support a polishing pad, a plurality of carrier heads suspended from and movable along a track such that each polishing station is selectively positionable at the stations, and a controller configured to control motion of the carrier heads along the track such that during polishing at each polishing station only a single carrier head is positioned in the polishing station.