We identify and analyze several performance problems in a state-of-the-art physically-based soft shadow volume algorithm, and present an improved method that alleviates these problems by replacing an overly conservative spatial acceleration structure by a more efficient one. The new technique consistently outperforms both the previous method and a ray tracing-based reference solution in several realistic situations while retaining the correctness of the solution and other desirable characteristics of the previous method. These include the unintrusiveness of the original algorithm, meaning that our method can be used as a black-box shadow solver in any offline renderer without requiring multiple passes over the image or other special accommodation. We achieve speedup factors