The progressive transition from Excimer to extreme ultraviolet (EUV) lithography is driving a need for flatter and smoother photomask blanks. It is, however, proving difficult to meet the next-generation specification with the conventional chemical mechanical polishing technology commonly used for finishing photomask blanks. This paper reports on the application of subaperture computer numerical control precessed bonnet polishing technology to the corrective finishing of photomask substrates for EUV lithography. Full-factorial analysis was used to identify process parameters capable of delivering microroughness below 0.5 nm rms while retaining relatively high removal rates. Experimental results show that masks prepolished to 300-600 nm peak-to-valley (P-V) flatness by chemical/mechanical polishing can then be improved down to 50-100 nm P-V flatness using the automated technology described in this paper. A series of edge polishing experiments also hints at the possibility of increasing the quality area beyond the 142 mm square defined in the official EUV photomask specification.