Since the 2003 Annual Meeting, the Precessions process has become accepted as an efficient method for polishing and figuring moderate-sized axially-symmetric aspheric parts in industry. In this paper, we report on some very significant new advances beyond this capability. The first is the demonstration of the process on substantially larger diameter parts than worked hitherto - in particular, a precision-ground 500mm diameter deeply-concave aspheric mirror. We describe the consequences of polishing large parts with the axis of the part vertical, in contrast to the horizontal axis of the smaller machines. Issues include slurry puddling and settlement in concave forms, process-uniformity, adequate support of the part and handling. We then report on recent work developing the Precessions process for non axially-symmetric surfaces including free-form. The correct relationship of the process with metrology has proved to be complex on several fronts, one example being differing descriptions of form either along a surface or its projection. We present our experience using profilometry and interferometry on precision-ground and polished surfaces, and in achieving absolute form with known base radius. Finally, we remark on the potential power of a priori predictions of achievable surface quality when optimizing optical system designs.© (2004) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.