Nineteen analytic potential energy functions (PEFs) for aluminum (three pairwise additive ones, six nonpairwise additive ones with three-body terms, and ten embedded atom-type PEFs) were obtained from the literature. The PEFs were tested and reparametrized using a diverse training set that includes 20 potential energy curves and a total of 224 geometries for five aluminum clusters Al N (N = 2, 3, 4, 7, and 13) computed using hybrid density functional theory, as well as the experimental face-centered cubic cohesive energy and lattice constant. The best PEFs from the literature have mean unsigned errors (MUEs) over the clusters in the data set of ∼0.12 eV/atom. The best reparametrized PEFs from the literature have MUEs of 0.06 eV/atom. The data set is also used to develop, parametrize, and systematically study the effectiveness of several functional forms designed specifically to model many-body effects in clusters, including bond angle, screening, and coordination number effects; a total of eighteen new PEFs are proposed and tested. The best potential overall has an MUE of 0.05 eV/atom, explicitly includes screening and coordination number effects, features linear scaling, and incorporates the accurate two-body and bulk limits.