Most 3D mesh generation techniques require simplification and mesh improvement stages to prepare a tetrahedral model for efficient simulation. We have developed an algorithm that both reduces the number of tetrahedra in the model to permit interactive manipulation and removes the most poorly shaped tetrahedra to allow for stable physical simulations such as the Finite Element Method. The initial tetrahedral model may be composed of several different materials representing internal structures. Our approach targets the elimination of poorly-shaped elements while simplifying the model using edge collapses and other mesh operations, such as vertex smoothing, tetrahedral swaps, and vertex addition. We present the results of our algorithm on a variety of inputs, including models with more than a million tetrahedra. In practice, our algorithm reliably reduces meshes to contain only tetrahedra that meet specified shape requirements, such as the minimum solid angle.