It has been demonstrated that modifying the rim scattering of a paraboloidal reflector antenna through the use of reconfigurable elements along the rim facilitates sidelobe modification including cancelling sidelobes. In this work we investigate several open questions with respect to algorithms for determining the weights. First, we derive the general weight values needed at each reconfigurable element to place nulls at arbitrary angles. Second, since in many cases these weights require gains other than one, we develop a technique for determining unit-modulus weights so as to allow for surfaces which merely modify the phase of the scattered field, while substantially reducing the gain at arbitrary angles. Specifically, it is shown that despite the large search space (and non-convexity in the presence of discrete weights), weights can be found with reasonable computational complexity which provide useful cancellation capability. Third, it is demonstrated that this can be done using open-loop (i.e., with pattern knowledge), closed-loop (without pattern knowledge), or hybrid (with inexact pattern knowledge) techniques both quantized and unquantized phases. A primary finding is that sufficiently deep nulls are possible with essentially no change in the main lobe gain with practical (binary or quaternary) phase-only weights.