We present a parallel algorithm for minimizing molecular energy potential functions applied to the case of pure Lennard-Jones clusters. The algorithm demonstrates the combination of discrete, latticebased optimization with continuous optimization (relaxation) techniques. The suggested approach is not restricted to the Lennard-Jones potential and is aimed at problems in which the potential of interest may be significantly more costly than the Lennard-Jones. The intended audience includes researchers interested in practical computational problems involving minimum energy cluster conformation, such as may arise in catalysis, and those interested in algorithm development. The advantage of the algorithm is that the time required to find the minimum-energy structure for a relatively large cluster reduces to that of an interactive session. Our parallel implementation is capable of determining the best-known, previously published binding energies for n ≤ 150 LJ clusters in a matter of seconds and has provided new results on minimum energies for clusters of up to n - 1000 atoms using a massivelyparallel processor, the Thinking Machines CM-5.