In many applications, volumetric data sets are examined by displaying isosurfaces, surfaces where the data, or some function of the data, takes on a given value. Interactive applications typically use local lighting models to render such surfaces. This work introduces a method to precompute or lazily compute global illumination to improve interactive isosurface renderings. The precompiled illumination resides in a separate volume and includes direct light, shadows, and intersections. Using this volume, interactive globally illuminated renderings of isosurfaces become feasible while still allowing dynamic manipulation of lighting, viewpoint and isovalue.