We have developed new potentials to model the interactions between H3O+ and H2O and used them to investigate small H3O...+(H2O)(n) clusters for n = 1 - 7. The construction of the potentials uses monomer properties for the long-range interactions and perturbation theory for the short-range terms. We have extensively searched all the potential energy surfaces and discuss the low-energy minima that we have found. We extend the calculations for n = 2, 4, and 5 by performing geometry optimizations using density functional theory, starting with minima found with the new model potential.