Dynamic modification of the pattern of a reflector antenna system traditionally requires an array of feeds. This paper presents an alternative approach in which the scattering from a fraction of the reflector around the rim is passively modified using, for example, an electronically-reconfigurable reflectarray. This facilitates flexible sidelobe modification, including sidelobe canceling, for systems employing a single feed. Applications for such a system include radio astronomy, where deleterious levels of interference from satellites enter through sidelobes. We show that an efficient reconfigurable surface occupying about 11% of the area of an axisymmetric circular paraboloidal reflector antenna fed from the prime focus is sufficient to null interference arriving from any direction outside the main lobe with little change in the main lobe characteristics. We further show that the required surface area is independent of frequency and that the same performance can be obtained using 1-bit phase control of the constituent unit cells for a reconfigurable surface occupying an additional 6% of the reflector surface.