We performed self-consistent calculations of the oscillating part of the ground-state energy of atoms and cations from Be through Ca, using Strutinsky's shell-correction method in the framework of the extended Kohn–Sham scheme. New “transition state” numbers in the Taylor series expansion of the ground-state energy are introduced, allowing the elimination of the second-order shell-correction term. We show that the application of this procedure yields practically identical results whether it is performed self-consistently or not, and even the first-order term of the shell-correction series gives a good approximation. Oscillations in the shell-correction energy of cations appear amplified with respect to those of the corresponding isoelectronic neutral atoms. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004