This paper is concerned with the problem of partitioning a three-dimensional polytope into a small number of elementary convex parts. The need for such decompositions arises in tool design, computer-aided manufacturing, finite-element methods, and robotics. Our main result is an algorithm for decomposing a polytope with n vertices and r reflex edges into O(n + r2) tetrahedra. This bound is asymptotically tight in the worst case. The algorithm is simple and practical. Its running time is O((n + r2) log r).