A chemical mechanical polishing system includes a platen to hold a polishing pad, a carrier head to hold a substrate against a polishing surface of the polishing pad, and a controller. The polishing pad has a polishing control groove. The carrier is laterally movable by a first actuator across the polishing pad and rotatable by a second actuator. The controller synchronizes lateral oscillation of the carrier head with rotation of the carrier head such that over a plurality of successive oscillations of the carrier head such that when a first angular swath of an edge portion of the substrate is at an azimuthal angular position about an axis of rotation of the carrier head the first angular swath overlies the polishing surface and when a second angular swath of the edge portion of the substrate is at the azimuthal angular position the second angular swath overlies the polishing control groove.