Summary This paper provides a progress-report on the development of the Precessions polishing process. This is a new small-tool polishing technique for producing aspheric forms and correcting spherical forms. Precessions polishing has been developed by Zeeko Ltd in collaboration with the Optical Science Laboratory at University College London and Loh Optikmaschinen. The Zeeko/Loh All machine (see figure below) has a capacity of 200mm diameter, and is targeted at industrial lenses and mirrors. The baseline of the PrecessionsTM process is a sub-diameter physical tool working the surface with a polishing slurry. Position and orientation of the tooling is controlled by a 7-axis CNC polishing machine that has been custom-designed for the purpose. The tool comprises an inflated, bulged, rubber-membrane (the 'bonnet'), covered with one of the usual proprietary flexible polishing surfaces familiar to opticians. The membrane moulds itself around the local asphere, keeping good contact everywhere. It is spun about its axis to give high removal-rates, and attacks the surface of the part working on the side of the bulged surface, rather than the classical pole-down configuration. The contact area and polishing pressure can be varied independently by changing the degree to which the bonnet is compressed, and the internal fluid pressure. The rotation axis is precessed around the local normal to the part, and this averages surface texture and achieves a near-Gaussian tool removal-profile (Influence function'). For axially-symmetric parts, the part is rotated and the tool moved radially, thereby creating a spiral tool-path. An off- line software application analyses i) the surface error-profile, and ii) experimental data on the tool influence functions for different spot-sizes. An iterative numerical optimisation method is then used to compute the dwell-time and spot- size for each zone of the spiral on the surface, to rectify the form error.