We propose a new formalism, Charge Model 2 (CM2), to obtain accurate partial atomic charges from a population analysis of wave functions by a parametrized mapping procedure, so that the resulting charges reproduce highly accurate charge-dependent observables. The new method, which produces class IV charges, is illustrated by developing CM2 mappings of Lowdin charges obtained from semiempirical and ab initio Hartree-Fock theory and density functional theory, in particular AM1, PM3, HF/MIDI!, HF/6-31G*, HF/6-31+G*, BPW91/MIDI!, BPW91/6-31G*, B3LYP/MIDI!, and BPW91/DZVP calculations. The CM2 partial charges reproduce experimental dipole moments with root-mean-square errors that are typically a factor of 7 better than dipole moments computed from Mulliken population analysis, a factor of 3 better than dipole moments computed by Lowdin analysis, and even a factor of 2 better than dipole moments computed from the continuous electron denisty. At the HF/6-31G* and B3LYP/MIDI! levels, the new charge model yields root-mean-square errors of 0.19 and 0.18 D, respectively, for the dipole moments of a set of 211 polar molecules containing a diverse range of structures and organic functional groups and the elements H, C, N, O, F, Si, P, S, Cl, Br, and I. A comparison shows that the new charge model predicts dipole moments more accurately than MP2/cc-pVDZ calculations, which are considerably more expensive. The quality of the results is similarly good for electrostatic potentials and for the other parametrizations as well.