Energy calculations have been carried out on high symmetry icosahedral and cuboctahedral Cu–Au nanoalloy clusters of various compositions, with the interatomic interactions modelled by the Gupta many-body potential. For each composition, the lowest energy isomers (“homotops”) tend to have predominantly Au atoms on the surface and Cu atoms in the core, and this phenomenon is explained in terms of surface energy, atomic size and trends in cohesive energies. A number of order parameters and mixing energies have been introduced and it is shown that there is good correlation between the cluster binding energy and the average distance of the Au atoms from the centre of the cluster. Comparisons are made with previous theoretical calculations on Cu–Au clusters, as well as with experimental studies of the structures and atom ordering of deposited Cu–Au particles.