We present a method for extreme occluder simplification. We take a triangle soup as input, and produce a small set of polygons with closely matching occlusion properties. In contrast to methods that optimize the original geometry, our algorithm has very few requirements for the input— specifically, the input does not need to be a watertight, two-manifold mesh. This robustness is achieved by working on a well-behaved, discretized representation of the input instead of the original, potentially badly structured geometry. We first formulate the algorithm for individual occluders, and further introduce a hierarchy for handling large, complex scenes.