The rapid estimation of basis set error and correlation energy from partial charges (REBECEP) method is improved further in several ways in the current paper. We introduce the total energies derived from experimental enthalpies of formation instead of G3 energies in,the fitting procedure. This increases the precision because the error of the G3 method is eliminated. We test the use of B3LYP/6-31G(d) equilibrium geometries instead of MP2/6-31G(d) geometries. This provides a considerable speed up. We also test the application of stockholder charges in the fitting procedure. New REBECEP parameters were obtained from HF/6-311+G(2dp) and HF/6-31G(d) energies and atomic charges (natural population analysis, Mulliken, and stockholder). A total of 117 closed shell neutral molecules from the G3/99 database composed of H, C, N, O, and F atoms were selected for the present study. While the correlation between various charges is reasonable for H, C, and N atoms, there, is a rather poor correlation between natural population analysis and stockholder charges for 0 and F atoms. The best REBECEP results were obtained using the HF/6-31G(d) natural population analysis charges. The root mean square and the average absolute deviations from the experimental enthalpies of formation for the selected 117 molecules are 2.16 and 1.65 kcal/mol, respectively. This is a considerable improvement as compared to our previous results (root mean square and average absolute deviations were 2.92 and 2.27 kcal/mol, respectively). The results are compared to Gaussian-3 and B3LYP/6-311+G(3df,2p) enthalpies of formation (the corresponding average absolute deviations for 51 large molecules are 0.94 and 7.09 kcal/mol, respectively). The REBECEP method performs considerably better for the 117 molecules with a moderate 6-31G(d) basis set than the B3LYP method with large 6-311+G(3df,2p) basis set.