The authors were required to fabricate small highly curved components with unusually deep asphericity together with extremely smooth and low damaged surfaces using lithium niobate, a crystalline material with anisotropic machining properties. Diamond-turning produced an accurate profile but with unacceptable roughness. Because existing CNC machines could not polish these surfaces adequately, a new polishing machine was developed. Three axes were controlled by a microcomputer to drive a very small rotating polishing tool over the rotating aspherical surface. The tool path was controlled to remove material uniformly from the surface or make corrections to surface profile.