Simulating 4D Simplicial Gravity including Degenerate Triangulations

We extend simulations of simplicial gravity in four dimensions to include {\it degenerate} triangulations and demonstrate that using this ensemble the geometric finite-size effects are much reduced. We provide strong numerical evidence for the existence of an exponential bound on the entropy of the model and establish that the phase structure is identical to that of a corresponding model restricted to an ensemble of combinatorial triangulations.