Small grinding and polishing tools are useful for certain applications since they can closely follow the curve of an aspheric surface and are less affected by workpiece distortion than larger tools. Also, the use of a computer to control the action of grinding and polishing tools can increase the efficiency and accuracy of the process. The computer controlled polisher (CCP) takes adantage of both features, moving a tool assembly with small pads over the workpiece under computer control. By varying the amount of time the machine works any region, a controlled amount of material may be removed. The best tool configuration for any figuring operation is determined by use of co puter modeling, while the proper operating parameters are obtained from ex perimentation. The process has been used to fabricate a nu her of difficult mirrors; as a result of this work, the CCP will be used on important future fabrication efforts.