The ability of the recently developed corrected equivalent core model (cECM) to predict properties of core hole states is examined for the CO molecule. It is shown that systematic corrections derived in this approach significantly improve the results of the conventional equivalent core model (ECM). This opens new possibilities to apply the equivalent core formalism to calculate the energy of core hole states which cannot be usefully done by the ECM itself. On the self-consistent-field level the predictions of geometry changes upon core ionization made by the cECM and those of direct core hole calculations are found to be very similar to each other. There exists, however, an appreciable difference between the total energies of the core hole states obtained in both approaches. A new procedure enabling us to improve the results of the cECM, in particular, to reduce this energy difference is proposed. In contrast to the cECM, where the corrections to the ECM energy are found by deriving the Hamiltonian H-Z of the Z system from the Hamiltonian HZ+1 of the (Z+1) system, the corrections are straightforwardly obtained in this new method (c(')ECM) by deriving HZ+1 from H-Z. The importance of the various systematic corrections to the ECM is discussed. (C) 2003 American Institute of Physics.