A tool (10) is disclosed for fine machining of optically active surfaces (F), with a base body (12) that can be attached to a tool spindle of a machine tool, and an elastic membrane (14) that has a machining section (16) to which connects a gaiter section (18) by means of which the membrane is attached to the base body such that it can be rotated therewith. The base body and the membrane delimit a pressure medium chamber (20) which via a channel (22) can be optionally pressurized with a pressure medium in order to apply a machining pressure via the machining section during machining of the optically active surface. A guide element (24) guided longitudinally mobile on the base body is actively connected with the machining section so that the machining section can be moved in the longitudinal direction of the guide element and held in the transverse direction to the guide element, although under an elastic deformation of the gaiter section it is tilt-mobile in relation to the guide element. The result is a tool of simple design and reliable function which has an excellent adaptability to a wide range of geometries to be machined.