A method for processing a rotationally symmetric workpiece, preferably having optically effective surfaces, whose symmetry axis is aligned parallel with the z-axis and which is moveable parallel with the z-axis, using a rotating, rotationally symmetric grinding or polishing tool whose rotation axis is aligned parallel with the y-axis and which is thereby touching the surface of the workpiece by means of a processing surface, the workpiece rotating around its symmetry axis and to a tool for performing said method as well as a method for tactile measuring of such a workpiece. The invention may be used for processing aspheric workpieces having optically effective surfaces, in particular lenses or mirrors that have a non-processable zone, for example a conical bump in the middle of the workpiece.