Compared to the correlation-consistent basis sets, it is not known if polarization-consistent pc-n basis sets, which were initially developed for HF and DFT calculations, can provide a monotonic and faster convergence toward the basis-set limit for results at correlated levels as well as better accuracy for a similar number of basis functions. It is also not known whether the pc-n basis sets can compute second derivatives of energy, such as nuclear magnetic shielding tensors, efficiently. To address these questions, the pc-n (n = 1-4), cc-pVxZ, and/or aug-cc-pVxZ (x = D, T, Q, 5, and 6) basis sets were used to compute the molecular and/or spectroscopic parameters of H-2, H2O, and NH3 at the RHF, B3-LYP, MP2, and/or CCSD(T) levels of theory. The results show that compared to the cc-pVxZ and/or aug-cc-pVxZ basis sets the pc-n basis sets yield faster convergence toward the basis-set limit but equivalent molecular and/or spectroscopic parameters in the basis-set limit at the RHF, DFT, MP2, and CCSD(T) levels. Because the pc-n basis sets show faster convergence, fewer basis-set functions are needed to reach the accuracy obtained with the aug-cc-pVxZ basis sets, enabling faster calculations and less computer storage space. The results also show that the pc-n basis sets, in conjunction with the "locally dense" basis-set approach, could be applied to predict accurate parameters; thus, they could be used to estimate accurate molecular or spectroscopic properties (e.g., NMR parameters) for larger systems such as the active site of enzymes.