Visibility determination is a key requirement in a wide range of graphics algorithms. This paper introduces a new approach to the computation of volume visibility, the detection of occluded portions of space as seen from a given region. The method is conservative and classifies regions as occluded only when they are guaranteed to be invisible. It operates on a discrete representation of space and uses the opaque interior of objects as occluders. This choice of occluders facilitates their extension into adjacent opaque regions of space, in essence maximizing their size and impact. Our method efficiently detects and represents the regions of space hidden by such occluders. It is the first one to use the property that occluders can also be extended into empty space provided this space is itself occluded from the viewing volume. This proves extremely effective for computing the occlusion by a set of occluders, effectively realizing occluder fusion. An auxiliary data structure represents occlusion in the scene and can then be queried to answer volume visibility questions. We demonstrate the applicability to visibility preprocessing for real-time walkthroughs and to shadow-ray acceleration for extended light sources in ray tracing, with significant acceleration in both cases.