Abstract: Monte Carlo integration is a powerful technique for the evaluation of difficult integrals. Applications in rendering include distribution ray tracing, Monte Carlo path tracing, and form-factor computation for radiosity methods. In these cases variance can often be significantly reduced by drawing samples from several distributions, each designed to sample well some difficult aspect of the integrand. Normally this is done by explicitly partitioning the integration domain into regions that are sampled differently. We present a powerful alternative for constructing robust Monte Carlo estimators, by combining samples from several distributions in a way that is provably good. These estimators are unbiased, and can reduce variance significantly at little additional cost. We present experiments and measurements from several areas in rendering: calculation of glossy highlights from area light sources, the "final gather" pass of some radiosity algorithms, and direct solution of the rendering equation using bidirectional path tracing.