  I define a model of three-dimensional simplicial gravity using an extended
ensemble of triangulations where, in addition to the usual combinatorial
triangulations, I allow degenerate triangulations, i.e. triangulations with
distinct simplexes defined by the same set of vertexes. I demonstrate, using
numerical simulations, that allowing this type of degeneracy substantially
reduces the geometric finite-size effects, especially in the crumpled phase of
the model, in other respect the phase structure of the model is not affected.
