The pairwise descreening approximation provides a rapid computational algorithm for the evaluation of solute shape effects on electrostatic contributions to solvation energies. In this article we show that solvation models based on this algorithm are useful for predicting free energies of solvation across a wide range of solute functionalities, and we present six new general parametrizations of aqueous free energies of solvation based on this approach. The first new model is based on SM2-type atomic surface tensions, the AM1 model for the solute, and Mulliken charges. The next two new models are based on SM5-type surface tensions, either the AM1 or the PM3 model for the solute, and Mulliken charges. The final three models are based on SM5-type atomic surface tensions and are parametrized using the AMI or the PM3 model for the solute and CM1 charges. The parametrizations are based on experimental data for a set of 219 neutral solute molecules containing a wide range of organic functional groups and the atom types H, C, N, O, F, P, S, Cl, Br, and I and on data for 42 ions containing the same elements. The average errors relative to experiment are slightly better than previous methods, but - more significantly - the computational cost is reduced for large molecules, and the methods are well suited to using analytic derivatives.