A complete set of Lennard Jones parameters for the halide ions, F-, Cl-, Br-, and I-, ammonium ion, and the alkali metal ions is reported. The parameters have been optimized using Monte Carlo simulations and free energy perturbation theory with the TIP4P water model to reproduce experimental free energies of hydration and locations of the first maxima of the ion-oxygen radial distribution functions, to provide water coordination numbers consistent with experimental ranges, and to exhibit gas-phase monohydrate energies in reasonable agreement with ab initio values. Average errors for absolute and relative free energies of hydration for the ions are ca. 1 kcal/mol. For the halides, this is the first self-consistent set of parameters that has been optimized for aqueous-phase performance. The good results for relative free energies of hydration are particularly auspicious for use of the new parameters in a wide variety of liquid-phase simulations where halide and alkali cations are systematically varied.