A device for fine processing of optically effective surfaces on workpieces has a workpiece spindle which protrudes into a working space and by which a workpiece to be polished can be rotationally driven about a workpiece axis of rotation. Two tool spindles are associated with the workpiece spindle and protrude into the working space oppositely to the workpiece spindle. On each tool spindle, a polishing tool can be rotationally driven about a tool axis of rotation and is retained so that the polishing tool can be axially advanced along the tool axis of rotation. Furthermore, the tool spindles can be moved together in relation to the workpiece spindle along a linear axis extending substantially perpendicularly to the workpiece axis of rotation and can be pivoted about different pivoting adjustment axes, which extend substantially perpendicularly to the workpiece axis of rotation and substantially perpendicularly to the linear axis.