Scaling all correlation (SAC) and multicoefficient correlation methods (MCCMs) have been shown to provide excellent ratios of accuracy to cost for the calculation of atomization energies. Inspired by this success, we have now fine-tuned the choices of correlation-energy levels and basis sets to determine the four most promising MCCMs and the most promising SAC method, and we optimized them against a larger and more diverse database than has previously been used for MCCM methods; the new database, called Database/3, consists of atomization energies, ionization potentials, electron affinites, and reaction barrier heights. The end results of this process are labeled as MCCM-version 3 (or MCCM/3) and SAC/3; the members of MCCM/3 are labeled MC-CO/3, MC-UT/3, MC-QCISD/3, and MCG3/3. The new methods are compared to other single-level ab initio methods, to hybrid density functional theory, and to the G3, G3S, and CBS-Q schemes. For neutral molecules, the mean unsigned error in atomization energies per bond using the SAC/3, MC-CO/3, MC-UT/3, MC-QCISD/3, and MCG3/3 methods are 1.4, 0.7, 0.5, 0.4, and 0.2 kcal/mol respectively, and these errors as well as the mean unsigned errors in ionization energies, electron affinites, and barrier heights compare very well with those in previous methods with higher costs.