We present candidate structures for the global minima of N-atom rare gas clusters containing one additional alkali metal ion, LJ(N)M. Lennard-Jones and Mason-Schamp potentials are used to represent the rare gas-rare gas and rare gas-alkali metal ion interactions, respectively. Results are presented for parameters appropriate to both Ar-K+ and Xe-Cs+ systems. When the ion is closer in size to the rare gas atoms (for XeNCs+) the global minima tend to be based on icosahedral packing. However, when the ion is relatively small (for ArNK+) the global minima below a certain size threshold are based on structures where the ion has lower coordination numbers. For larger clusters the global minima are again based on icosahedral packing. The latter structures can be found with minimal computational effort using the known global minima for clusters bound by Lennard-Jones or Morse potentials, substituting one atom at a time by the ion and minimizing. (C) 2003 American Institute of Physics.