We report on progress developing the Precession Process, that has recently been embodied for the first time in a fully-productionised aspheric polishing machine. We describe how the process uses inflated polishing tools of continuously-variable size and hardness. Despite the rapid tool rotation needed to give high removal rates, the method produce well-behaved and near-Gaussian tool influence functions, by virtue of the precession of the spin axis. We then describe how form errors are controlled. The method takes influence-function data and an error map as input, together with, uniquely, weighting factors for height and slope residuals and process time. A numerical optimisation of the cost function with variable dwell time, tool path and tool size is then performed. The advantages of this new technique are contrasted with conventional deconvolution methods. Results of form control on aspheric surfaces are presented, with an interpretation in terms of spatial frequencies. We draw particular attention to control of form at the centre and periphery of a workpiece. Finally, we describe how Precession processing gives multi- directional rubbing of surfaces, and we present the superb texture achieved on samples.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.