A carrier head for chemical mechanical polishing includes a base assembly and a membrane assembly connected to the base assembly. The membrane assembly includes a membrane support, an inner membrane secured to the membrane support, wherein the inner membrane forms a plurality of individually pressurizable inner chambers between an upper surface of the membrane and the membrane support, and an outer membrane secured to the membrane support and extending below the inner membrane, the outer membrane having an inner surface and an outer surface, wherein the outer membrane defines a lower pressurizable chamber between the inner surface of the outer membrane and a lower surface of the inner membrane, wherein the inner surface is positioned for contact by a lower surface of the inner membrane upon pressurization of one or more of the plurality of chambers, and wherein the outer surface is configured to contact a substrate.