We show how importance-driven refinement and a wavelet basis can be combined to provide an efficient solution to the global illumination problem with glossy and diffuse reflections. Importance is used to focus the computation on the interactions having the greatest impact on the visible solution. Wavelets are used to provide an efficient representation of radiance, importance, and the transport operator. We discuss a number of choices that must be made when constructing a finite element algorithm for glossy global illumination. Our algorithm is based on the standard wavelet decomposition of the transport operator and makes use of a four-dimensional wavelet representation for spatially and angularly varying radiance distributions. We use a final gathering step to improve the visual quality of the solution. Features of our implementation include support for curved surfaces as well as texture-mapped anisotropic emission and reflection functions.