The effect of 1s core correlation on properties and energy separations has been analyzed using full configuration-interaction (FCI) calculations. The Be 1S–1P, the C 3P–5S, and CH+ 1Σ+–1Π separations, and CH+ spectroscopic constants, dipole moment and 1Σ+–1Π transition dipole moment have been studied. The results of the FCI calculations are compared to those obtained using approximate methods. In addition, the generation of atomic natural orbital (ANO) basis sets, as a method for contracting a primitive basis set for both valence and core correlation, is discussed. When both core–core and core–valence correlation are included in the calculation, no suitable truncated CI approach consistently reproduces the FCI, and contraction of the basis set is very difficult. If the (nearly constant) core–core correlation is eliminated, and only the core–valence correlation is included, CASSCF/MRCI approaches reproduce the FCI results and basis set contraction is significantly easier.