We propose a new algorithm for rigid body simulation that guarantees each body is in an interpenetration free state, both increasing the accuracy and robustness of the simulation as well as alleviating the need for ad hoc methods to separate bodies for subsequent simulation and rendering. We cleanly separate collision and contact resolution such that objects move and collide in the first step, with resting contact handled in the second step. The first step of our algorithm guarantees that each time step produces geometry that does not intersect or overlap by using an approximation to the continuous collision detection (and response) problem and, thus, is amenable to thin shells and degenerately flat objects moving at high speeds. In addition, we introduce a novel fail-safe that allows us to resolve all interpenetration without iterating to convergence. Since the first step guarantees a noninterfering state for the geometry, in the second step we propose a contact model for handling thin shells in proximity considering only the instantaneous locations at the ends of the time step.