A retainer is used with an apparatus for polishing a substrate. The substrate has upper and lower surfaces and a lateral, substantially circular, perimeter. The apparatus has a polishing pad with an upper polishing surface for contacting and polishing the lower face of the substrate. The retainer has an inward facing retaining face for engaging and retaining the substrate against lateral movement during polishing of the substrate. The retaining face engages a substrate perimeter at more than substantially a single discrete circumferential location along the perimeter.