We present eight new parameterizations of the SM5.42R solvation model: in particular we present parameterizations for HF/MIDI!, HF/6-31G*. HF/6-31 + G*, HF/cc-pVDZ, AM1, PM3, BPW91/MIDI!, and B3LYP/MIDI!. Two of the new cases are parameterized using the reaction-field operator presented previously, and six of the new cases are parameterized with a simplified reaction-field operator; results obtained by the two methods are compared for selected examples. For a training set of 2135 data for 275 neutral solutes containing H, C, N, O, F, S, P, Cl, Br, and I in 91 solvents (water and 90 nonaqueous solvents), seven of the eight new parameterizations give mean unsigned errors in the range 0.43-0.46 kcal/mol, and the eighth - for a basis set containing diffuse functions - gives a mean unsigned error of 0.53 kcal/mol. The mean unsigned error for 49 ionic solutes (containing the same elements) in water is 3.5-3.9 kcal/mol for the Hartree-Fock, Becke-Perdew-Wang-1991 and Becke three-parameter Lee-Yang-Parr cases and 4.1 and 4.0 kcal/mol for parameterized model 3 and Austin model 1, respectively. The methods are tested for sensitivity of solvation free energies to geometry and for predicting partition coefficients of carbonates, which were not included in the training set.