A carrier head for holding a substrate in a polishing system includes a housing, a first flexible membrane secured to the housing to form one or more pressurizable chambers to apply pressure through a central membrane portion of the first flexible membrane to a central portion of a substrate, and a plurality of independently operable piezoelectric actuators supported by the housing, the plurality of piezoelectric actuators positioned radially outward of the central membrane portion and at different angular positions so as to independently adjust pressure on a plurality of angular zones in an annular outer region of the substrate surrounding the central portion of the substrate.