A carrier head for a chemical mechanical polishing apparatus includes a carrier body, an outer membrane assembly, an annular segmented chuck, and an inner membrane assembly. The outer membrane assembly is supported from the carrier body and defines a first plurality of independently pressurizable outer chambers. The annular segmented chuck supported below the outer membrane assembly, and includes a plurality of concentric rings that are independently vertically movable by respective pressurizable chambers of the outer membrane assembly. At least two of the rings having passages therethrough to suction-chuck a substrate to the chuck. The inner membrane assembly is supported from the carrier body and is surrounded by an innermost ring of the plurality of concentric rings of the chuck. The inner membrane assembly defines a second plurality of independently pressurizable inner chambers and has a lower surface to contact the substrate.