Shading complex materials such as acquired reflectances in multi-light environments is computationally expensive. Estimating the shading integral involves stochastic sampling of the incident illumination independently at several pixels. The number of samples required for this integration varies across the image, depending on an intricate combination of several factors. Ignoring visibility, adaptively distributing computational budget across the pixels for shading is already a challenging problem. In this paper we present a systematic approach to accelerate shading, by rapidly predicting the approximate spatial and angular variation in the local light field arriving at each pixel. Our estimation of variation is in the form of local bandwidth, and accounts for combinations of a variety of factors: the reflectance at the pixel, the nature of the illumination, the local geometry and the camera position relative to the geometry and lighting. The speed-up, using our method, is from a combination of two factors. First, rather than shade every pixel, we use this predicted variation to direct computational effort towards regions of the image with high local variation. Second, we use the predicted variance of the shading integrals, to cleverly distribute a fixed total budget of shading samples across the pixels. For example, reflection off specular objects is estimated using fewer samples than off diffuse objects.