Abstract: This paper presents an efficient algorithm for filtering multi-layer depth images (MDIs) in order to produce approximate penumbras. The filtering is performed on a MDI that represents the view from the light source. The filtering process can be shown to approximate the tracing of shadow rays through the MDI. The method is based upon the z-buffer shadow algorithm, and is closely related to convolution methods for producing penumbras. It is shown how the alteration of filter weights can produce interesting shadow effects, including the simulation of several lights at once. The method's effectiveness is demonstrated on especially complex objects such as trees, whose soft shadows are expensive to compute by other methods. The method specifically addresses the problem of light-leaking that occurs when tracing rays through discrete representations, and the inability of convolution methods to produce accurate self-shadowing effects.