Parametric studies to optimize heavy-ion driver designs are described and an optimized 5 MJ driver design is described. Parametric studies are done on driver parameters including driver energy, number of beams, type of superconductor used in focusing magnets, maximum magnetic field allowed at the superconducting windings, axial quadrupole field packing fraction, ion mass, and ion charge state. All modeled drivers use the maximum beam currents allowed by the Maschke limits; driver scaling is described in a companion paper. The optimized driver described is conservative and cost effective. The base driver direct costs are only $120/Joule, and the base driver uses no recirculation, beam combination, or beam separation. The low driver cost we achieve is due, in part, to the use of compact Nb3Sn quadrupole arrays, but results primarily from optimization over the large, multi-dimensional, parameter space available for heavy-ion drivers.