Many compelling applications would become feasible if novice users had the ability to synthesize high quality human motion based only on a simple sketch and a few easily specified constraints. Motion graphs and their variations have proven to be a powerful tool for synthesizing human motion when only a rough sketch is given. Motion graphs are simple to implement, and the synthesis can be fully automatic. When unrolled into the environment, motion graphs, however, grow drastically in size. The major challenge is then searching these large graphs for motions that satisfy user constraints. A number of sub-optimal algorithms that do not provide guarantees on the optimality of the solution have been proposed. In this paper, we argue that in many situations to get natural results an optimal or nearly-optimal search is required. We show how to use the well-known A* search to find solutions that are optimal or of bounded sub-optimality. We achieve this goal for large motion graphs by performing a lossless compression of the motion graph and implementing a heuristic function that significantly accelerates the search for the domain of human motion. We demonstrate the power of this approach by synthesizing optimal or near optimal motions that include a variety of behaviors in a single motion. These experiments show that motions become more natural as the optimality improves.