Abstract: The accurate generation of soft shadows is a particularly computationally intensive task. In order to reduce rendering time, most real-time and offline applications decorrelate the generation of shadows from the computation of lighting. In addition to such approximations, they generate shadows using some restrictive assumptions only correct in very specific cases, leading to penumbra over-estimation or light-leaking artifacts. In this paper we present an algorithm that produces soft shadows without exhibiting the previous drawbacks. Using a new efficient evaluation of the number of occluders between two points (i.e. the depth complexity) we either modulate direct lighting or numerically solve the rendering equation for direct illumination. Our approach approximates shadows cast by semi-opaque occluders and naturally handles area lights with spatially varying luminance. Furthermore, depending on the desired performance and quality, the resulting shadows are either very close to, or as accurate as, a ray-traced reference. As a result, the presented method is well suited to many domains, ranging from quality-sensitive to performance-critical applications.