We introduce an impostor-based visibility technique to provide approximate, average visibility for point-to-cluster and cluster-to-cluster visibility queries. Processing each object in a view-independent manner allows us to generate a mip-map-like hierarchy of approximate visibility information that can report approximate average visibility over conical shafts or conical shaft frustums. We demonstrate how these impostors can be used to approximate smooth soft shadow calculation, and improve the quality of lightcuts and multidimensional lightcuts. In addition, we describe how to use approximate visibility of shafts to estimate a tighter error bound for the lightcuts visibility term, yielding speedup by reducing over-aggressive cut refinement.