When a rigid polishing tool is moved in a radial direction on an aspheric surface, it will not fit the surface throughout the stroke. The nonuniform pressure under the tool as a result of this misfit will result in a nonuniform removal of material and thus alter the shape of the aspheric surface. This result may be avoided by providing for some flexibility in the tool. A tool consisting of a rigid backing, a soft resilient layer, a thin layer of selected flexural rigidity and finally a thin layer of polishing pitch will provide such flexibility. For a given aspheric the material and thickness of the controlling layer may be selected, depending on tool size and shape and the stroke desired so that the variation of pressure on the optical surface may be made acceptably small. However, sufficient rigidity is retained to provide rapid smoothing action. Thus, the use of such tools result in smooth aspheric surfaces. Some large optical mirrors are constructed of thin face plates separated by a ribbed core structure in the interests of light weight. Because the face plate deflects under the polishing pressure, the areas over the ribs are polished away faster than other areas. The composite tool described here reduces this effect as the resilient layer is made softer and the tool larger. Properly designed tools then permit the polishing and smoothing of large aspherics with thinner face plates and thus, lighter than has been required by previous polishing methods.