A process is provided for producing near-perfect optical surfaces, for EUV and soft-x-ray optics. The method involves polishing or otherwise figuring the multilayer coating that has been deposited on an optical substrate, in order to correct for errors in the figure of the substrate and coating. A method such as ion-beam milling is used to remove material from the multilayer coating by an amount that varies in a specified way across the substrate. The phase of the EUV light that is reflected from the multilayer will be affected by the amount of multilayer material removed, but this effect will be reduced by a factor of 1−n as compared with height variations of the substrate, where n is the average refractive index of the multilayer.