Methods and apparatus provide for a conformable polishing head for uniformly polishing a workpiece. The polishing head includes an elastic polishing pad mounted on an elastic membrane that seals a cavity in the polishing head. The cavity is pressurized to expand the membrane and press the polishing pad down on the top surface of the workpiece, such that the polishing pad conforms to the surface and applies a substantially uniform pressure distribution across the workpiece and thereby uniformly removes material across high and low spots on the workpiece.