The scroll elements of a scroll-type compressor are treated employing a lapping tool to achieve increased flatness of the base surface and increased smoothness of the side walls of the involute wrap. This reduces flank leakage, tip leakage, and thrust friction losses. The lapping device that is placed against the scroll element has a radially extending base and a generally spiral wrap, the wrap generally matching that of the scroll element workpiece. The lapping device wrap has axially erect walls and a radially flat tip surface. After engaging the scroll element work piece, the lapping device is moved relative to the scroll element in an orbiting motion. A suitable lapping compound is introduced at least between the lapping device wrap tip surface and the base surface of the scroll element, and, if desired, also between the side walls of the lapping device wrap and the side walls of the scroll element wrap. The lapping compound can be introduced directly or in a gas flow.