1993 is employed to calculate the Kohn᎐Sham KS potential, V , for the exchange-only x case in which the electron᎐electron interaction between ''core'' electrons in the Ž . Hartree᎐Fock exchange energy functional is treated in the local-spin-density LSD Ž . Ž . approximation with and without self-interaction-correction SIC . The resulting V r x maintains the important analytic properties exhibited by the exact KS potential. When the core is taken to include all occupied states except those in the last two occupied subshells of the atom, we find that properties strongly dependent on the valence electron states continue to be accurately approximated. In particular, when the LSDSIC approximation is employed, we find the results of self-consistent calculations of the ionization potential and electron affinity are within 0.3 mRy of the exact KS results and that the energy ² 2 : eigenvalue corresponding to the highest energy occupied orbital and r have an average error of a few tenths of 1% for both atoms and negative ions for Z F 20. Similarly, slightly less accurate results are obtained when the LSD approximation is employed. These results suggest that the KLI method may be accurately and more easily applied to multiatom systems when this additional approximation is made.