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.