The prevailing approach in density-functional theory makes use of universal functionals, valid for any number of electrons (N). In this article and following the work of Lieb [E. H. Lieb, Int. J. Quantum Chem. 24, 243 (1983)], we argue that the use of N-dependent functionals could be an equally valid approach. Size consistency (dissociation into proper fragments) puts restrictions on the form that N-dependent functionals may adopt. We propose a simple procedure for correcting the size-consistency problem of existing N-dependent functionals that also provides an original way of designing new ones. (C) 2001 American Institute of Physics.