The major source of error in most ab initio calculations of molecular energies is the truncation of the one-electron basis set. Extrapolation to the complete basis set second-order (CBS2) limit using the N-1 asymptotic convergence of N-configuration pair natural orbital (PNO) expansions can be combined with the use of relatively small basis sets for the higher-order (i.e., MP3, MP4, and QCI) correlation energy to develop cost effective computational models. Following this strategy, three new computational models denoted CBS-4, CBS-q, and CBS-Q, are introduced. The mean absolute deviations (MAD) from experiment for the 125 energies of the G2 test set are 2.0, 1.7, and 1.0 kcal/mol, respectively. These results compare favorably with the MAD for the more costly G2(MP2), G2, and CBS-QCI/APNO models (1.6, 1.2, and 0.5 kcal/mol, respectively). The error distributions over the G2 test set are indistinguishable from Gaussian distribution functions for all six models, indicating that the rms errors can be interpreted in the same way that experimental uncertainties are used to assess reliability. However, a broader range of examples reveals special difficulties presented by spin contamination, high molecular symmetry, and localization problems in molecules with multiple lone pairs on the same atom. These characteristics can occasionally result in errors several times the size expected from the Gaussian distributions. Each of the CBS models has a range of molecular size for which it is the most accurate computational model currently available. The largest calculations reported for these models include : The CBS-4 heat of formation of tetranitrohydrazine (91.5 +/- 5 kcal/mol), the CBS-4 and CBS-q isomerization energies for the ;conversion of azulene to naphthalene (Delta H-calc = -35.2 +/- 1.0 kcal/mol, Delta H-exp = -35.3 +/- 2.2 kcal/mol), and the CBS-Q heat of formation of SF6 (Delta H-calc = -286.6 +/- 1.3 kcal/mol, Delta H-exp = -288.3 +/- 0.2 kcal/mol). The CBS-Q value for the dissociation energy of a C-H bond in benzene (113.1 +/- 1.3 kcal/mol) is also in agreement with the most recent experimental result (112.0 +/- 0.6 kcal/mol). The CBS-QCI/APNO model is applicable to the prediction of the C-H bond dissociation energies for the primary (100.7 +/- 0.7 kcal/mol calc.) and secondary (97.7 +/- 0.7 kcal/mol calc., 97.1 +/- 0.4 kcal/mol exp.) hydrogens of propane.