Abstract: In this paper, we address the problem of computing the radiance in a diffuse environment up to a beforehand specified accuracy. We consider this problem in the context of wavelet radiosity, a hierarchical radiosity method with higher order radiance approximations. We first present an analysis of the discretization error, which is the error introduced by projecting the problem onto a finite set of basis functions. This analysis leads to an algorithm for a-posteriori error estimation and a criterion and strategy for hierarchical refinement, generalising previous work for constant and bilinear approximations. We propose a new hierarchical radiosity algorithm in which a user controls the accuracy of the solution by specifying directly the maximum allowable absolute radiance error rather than an interaction error threshold.