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This paper introduces a new approximation algorithm for the near-field ambient occlusion problem. It combines known pieces in a new way to achieve substantially improved quality over fast methods and substantially improved performance compared to accurate methods. Intuitively, it computes the analog of a shadow volume for ambient light around each polygon, and then applies a tunable occlusion function within the region it encloses. The algorithm operates on dynamic triangle meshes and produces output that is comparable to ray traced occlusion for many scenes. The algorithm's performance on modern GPUs is largely independent of geometric complexity and is dominated by fill rate, as is the case with most deferred shading algorithms.