The stressed-lap polishing technique has been developed to meet the challenge of polishing 8- m-class mirrors with highly aspheric figures to an accuracy consistent with the best ground- based telescope sites. The method is currently being demonstrated in the polishing of two primary mirrors, a 1.8-m f/1.0 ellipsoid and a 3.5-m f/1.5 paraboloid. The figure accuracies achieved at the time of writing are 43 nm rms surface error for the 1.8-m mirror, and 190 nm rms surface error for the 3.5-m mirror. Polishing is proceedings on both mirrors. In this paper we describe the process used for the 3.5-m mirror and the progress through the early stages of fabrication. We also summarize progress on the 1.8-m mirror.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.