Abstract: Shadow mapping is a technique for doing real-time shadowing. Recent work has shown that shadow mapping hardware can be used as a second depth test in addition to the z-test. In this paper, we explore the computational power provided by this second depth test by examining the problem of rendering objects described as CSG (Constructive Solid Geometry) expressions. We provide an algorithm that asymptotically improves the number of rendering passes required to display a CSG object by a factor of n by exploiting the two-sided depth test. Interestingly, a matching lower bound can be proved demonstrating that our algorithm is optimal.