We present an improved radiosity method for accounting for non-Lambertian reflections. The method explicitly calculates the radiance distribution leaving each non-Lambertian surface. The method differs from previous explicit radiosity methods in two respects. First, non-Lambertian surfaces are discretized adaptively based on their effect on other surfaces, rather than on their own spatial radiance distribution. Second, the calculation of the radiance distribution for surfaces that are neither Lambertian nor mirror-like surfaces is made more efficient using the ideas of hemi-cube pixel groups and the reflectance hemisphere. The method is well suited to being used as the first pass in a multi-pass rendering method.