Abstract: We present an efficient method for importance sampling the product of multiple functions. Our algorithm computes a quick approximation of the product on the fly, based on hierarchical representations of the local maxima and averages of the individual terms. Samples are generated by exploiting the hierarchical properties of many low-discrepancy sequences, and thresholded against the estimated product. We evaluate direct illumination by sampling the triple product of environment map lighting, surface reflectance, and a visibility function estimated per pixel. Our results show considerable noise reduction compared to existing state-of-the-art methods using only the product of lighting and BRDF.