A retaining ring is configured for use with an apparatus for polishing a substrate. The substrate has upper and lower faces and a perimeter. The apparatus has a movable polishing pad with an upper polishing surface for contacting and polishing the lower face of the substrate. The retaining ring has a retaining face for engaging and retaining the substrate against lateral movement and a bottom face for contacting the polishing surface of the polishing pad. The bottom face of the retaining ring extends downward from an inner portion adjacent the retaining face to a lowermost portion radially outboard of the retaining face.