Retaining ring with convex bottom surface

A retaining ring for a chemical polisher comprises a generally annular body having a top surface (115), an inner diameter surface (235), an outer diameter surface (230) and a bottom surface (155), wherein the bottom surface has a convex shape and wherein a difference in height across the bottom surface is between 0.001 mm and 0.05 mm. A method of using a retaining ring comprises lapping a bottom surface of an annular retaining ring to provide a target characteristic, the lapping being performed using a first machine dedicated for use in lapping the bottom surface of retaining rings; securing the retaining ring on a carrier head; and polishing a plurality of device substrates with a second machine using the carrier head, wherein the target surface characteristic substantially matches an equilibrium surface characteristic that would result from breaking-in the retaining ring on the second machine.