Primary mirrors for large aperture telescopes (> 10 m) are collections of smaller (1-2 m), typically hexagonal, often aspheric, optical segments. NASA's next generation specifications demand high precision optical surfaces with practically zero edge exclusion in order to maximize image contrast and resolution. Magnetorheological finishing (MRF) is a sub-aperture process demonstrated to be effective for fine figure control and polishing of a variety of optical glasses and crystals. The relatively small size and high removal rate of the MRF tool could allow efficient correction of "print-through" patterns (or other mid-spatial frequency errors) often observed after conventional polishing. MRF, however, can suffer from edge effects, because the MRF polishing spot changes as it moves over the edge of the part. Current control algorithms assume the spot remains constant, resulting in edge errors on the order of half of the spot size in width. In Phase I, we identified a promising method of counteracting edge effects. In Phase II, we will develop, test, and refine three software- and process-based solutions, and apply them to polishing an optic of relevance to NASA's needs.