A flexible membrane for a carrier head of a chemical mechanical polisher includes a main portion, an annular outer portion, and three annular flaps. The main portion has a substrate mounting surface with a radius R. The annular outer portion extends upwardly from an outer edge of the main portion and has a lower edge connected to the main portion and an upper edge. The three annular flaps include a first annular flap joined to an inner surface of the main portion at a radial position between 75% and 95% of R, a second inwardly-extending annular flap joined to the annular outer portion at a position between the lower edge and the upper edge, and a third inwardly-extending annular flap joined to the upper edge of the annular outer portion.