A procedure for calculating core-electron binding energies (CEBEs), based on a total-energy difference approach within Kohn-Sham density functional theory, was investigated. Ten functional combinations and several basis sets (including unscaled, scaled, and core-valence correlated functions) were studied using a database of reliable observed CEBEs. The functionals designed by Perdew and Wang (1986 exchange and 1991 correlation) were found to give the best performance with an average absolute deviation from experiment of 0.15 eV. The scaled basis sets did not perform satisfactorily, but it was found that the core-valence correlated cc-pCVTZ basis functions were an excellent alternative to the cc-pV5Z set as they provided equally accurate results and could be applied to larger molecules.