Most visibility culling algorithms require convexity of occluders. Occluder synthesis algorithms attempt to construct large convex occluders inside bulky non-convex sets. Occluder fusion algorithms generate convex occluders that are contained in the umbra cast by a group of objects given an area light. In this paper we prove that convexity requirements can be shifted from the occluders to their umbra with no loss of efficiency, and use this property to show how some special non-planar, non-convex closed polylines that we call "hoops" can be used to compute occlusion efficiently for objects that have no large interior convex sets and were thus rejected by previous approaches.