The molecular and spectroscopic parameters calculated using the hybrid density functional B3PW91 are reported for a model set of compounds composed of H-2, N-2, NH3, CH4, C2H4, HCN, CH3CN, and H2O. An estimation of the DFT and Hartree-Fock complete basis-set limit (CBS) energy and NMR parameters from the 2- (3-) point exact fit versus least-squares fit (NLLSQ) was obtained with the cc-pVxZ and aug-cc-pVxZ basis sets (x = D, T, Q, 5, 6). A marginally faster convergence of the fitted parameters obtained with core-valence basis sets cc-pCVxZ and aug-cc-pCVxZ was noticed. The Hartree-Fock-predicted CBS heavy-atom isotropic shieldings of the model molecules, as compared with those of DFT, were closer to experiment. It was also shown that GIAO MP2-predicted NMR parameters yield the best agreement with those obtained from experiment and benchmark calculations. As. support for experimental studies, the CBS approach of calculating accurate nuclear shieldings of larger molecules is proposed.