Numerical atom-centered basis sets (orbitals) (NAO) are known for their compactness and rapid convergence in the Hartree–Fock and density-functional theory (DFT) molecular electronic-structure calculations. To date, not much is known about the performance of the numerical sets against the well-studied Gaussian-type bases in correlated calculations. In this study, one instance of NAO [Blum et al., The Fritz Haber Institute ab initio Molecular Simulations Package (FHI-aims), 2009] was thoroughly examined in comparison to the correlation-consistent basis sets in the ground-state correlated calculations on the hydrogen-bonded water and dispersion-dominated methane dimers. It was shown that these NAO demonstrate improved, comparing to the unaugmented correlation-consistent based, convergence of interaction energies in correlated calculations. However, the present version of NAO constructed in the DFT calculations on covalently-bound diatomics exhibits enormous basis-set superposition error (BSSE)—even with the largest bases. Moreover, these basis sets are essentially unable to capture diffuse character of the wave function, necessary for example, for the complete convergence of correlated interaction energies of the weakly-bound complexes. The problem is usually treated by addition of the external Gaussian diffuse functions to the NAO part, what indeed allows to obtain accurate results. However, the operation increases BSSE with the resulting hybrid basis sets even further and breaks down the initial concept of NAO (i.e., improved compactness) due to the significant increase in their size. These findings clearly point at the need in the alternative strategies for the construction of sufficiently-delocalized and BSSE-balanced purely-numerical bases adapted for correlated calculations, possible ones were outlined here. For comparison with the considered NAOs, a complementary study on the convergence properties of the correlation-consistent basis sets, with a special emphasis on BSSE, was also performed. Some of its conclusions may represent independent interest. © 2013 Wiley Periodicals, Inc.