We have developed an efficient and flexible algorithm that simultaneously calculates free energies for multiple compounds either reporting quantitative results to a desired precision or rapidly generating a qualitative ranking. When applied to a rest case analogous to competitive binding of multiple ligands to a common protein, our algorithm quickly (within a few picoseconds) identifies the ligand possessing the most favorable binding affinity. In a detailed iterative calculation of the free energy changes, our method is approximately twice as efficient as the standard FEP method. In fact, improved biasing potentials may further enhance the efficiency of the protocol.