A chemical mechanical polishing system includes a substrate support configured to hold a substrate, a polishing pad assembly include a membrane and a polishing pad portion having a polishing surface, a polishing pad carrier, and a drive system configured to cause relative motion between the substrate support and the polishing pad carrier. The polishing pad portion is joined to the membrane on a side opposite the polishing surface. The polishing surface has a width parallel to the polishing surface at least four times smaller than a diameter of the substrate. An outer surface of the polishing pad portion includes at least one recess and at least one plateau having a top surface that provides the polishing surface. The polishing surface has a plurality of edges defined by intersections between side walls of the at least one recess and a top surface of the at least one plateau.