The general structure of small fcc metal clusters was investigated through the use of site energies, i.e., interaction energy per atom as a function of coordination. We used only experimental data on the dimer binding energy, the surface energy, and the bulk cohesive energy to determine these energies for all 15 fcc metals. These showed that real fcc metal systems exhibit a slight bond weakening as the number of bonds increases. It is also demonstrated that experimental data are much closer to the limit of constant bond energy than to that of constant interaction energy per atom. The constant bond energy model leads to compact structures which maximize the number of bonds, and thus we predicted that real small cluster systems would also be compact. Using molecular dynamics/Monte Carlo corrected effective medium theory, which nearly duplicates the experimental site energy curves, we studied the structures of 13-atom clusters of fcc metals via repeated melting and quenching in computer simulations. The lowest-energy structure was found to be a compact icosahedron with very high symmetry in every case. We also performed such simulations in the presence of a SiO2 support and found that the 13-atom Pt cluster maintained its nearly icosahedral shape.