The application of the self-interaction-corrected local spin density approximation (SIC-LSDA) to atoms is reexamined. It is shown that a more careful application of the central-field approximation results in a modified functional which yields accurate total energies, correlation energies, and, in the "exchange-only" (X-O) version, exchange energies in good agreement with Hartree-Fock (HF) values. It is also shown that the X-O version of the earlier SIC-LSDA functional yields total energies in close agreement with experiment for second-row atoms. The proposed modification removes this tendency of the X-O functional to mimic a correlated functional. © 1983 American Institute of Physics.