A new variant of the so-called "cheap composite scheme" has been purposely developed for the evaluation of the interaction energy of non-covalent molecular complexes, with its various contributions being tested for a set of 15 systems using the accurate interaction energies reported in ref. [Rezac, J.; Dubecky, M.; Jurecka, P.; Hobza, P. Phys. Chem. Chem. Phys. 2015, 17, 19268-19277] as reference values. The modified scheme, starting from the CCSD(T) method in conjunction with a triple-zeta-quality basis set augmented by diffuse functions, includes two additional terms computed at the MP2 level: (i) the extrapolation to the complete basis set (CBS) limit; (ii) the contribution of core-valence correlation effects (CV term). Various families of basis sets including diffuse functions have been tested for the CCSD(T) model as well as for the extrapolation to the CBS limit, with a mean absolute error of about 1% (below 0.2 kJ·mol-1 in absolute terms) obtained with the jun-cc-pVnZ and the jul-cc-pVnZ families. As far as the CV term is concerned, the cc-pCVTZ and cc-pwCVTZ basis sets provide comparable contributions, which are non-negligible in several cases. While the benchmark analysis has been carried out using accurate structures available in the literature, geometrical effects due to the use of reference B2PLYP(-D3BJ) geometries, optimized in conjunction with a triple-ζ-quality basis set, have been investigated, thus pointing out their suitability. Finally, the modified scheme has been applied to a number of test cases for which interaction energies were already available in the literature; among these, a number of molecular complexes bearing second-row atoms have been considered.