We investigate the structures of clusters bound by the Morse potential by mapping the structure of the global minimum as a function of both cluster size and the range of the pair potential. We consider values of the range parameter appropriate to a loosely bound diatomic molecule (longest), two C-60 molecules (shortest), and at regular intervals between these two limits. We have studied all cluster sizes with 25 atoms or less and a selection of sizes containing between 35 and 80 atoms. The effect of decreasing the range of the potential is to destabilize strained structures. For the larger clusters the structure of the global minimum changes from icosahedral to decahedral to face-centered cubic as the range is decreased. We have also investigated the effects of temperature on the equilibrium structure by performing a model calculation for a 75-atom cluster.