A semi-empirical self-interaction correction, based on the fractional number of electrons q(A) surrounding each atom A, is investigated in generalised gradient approximation density functional theory. The correction, which involves locally scaling the exchange functional (Becke 1988) by q(A)(0.371), leads to a significantly improved potential energy curve for H-2(+). It also shifts the H-2 potential energy curve towards that of Hartree-Fock, and increases the barrier for the reaction H + H-2-->H-2 + H. An alternative correction q(A)(-0.174) leads to a much improved dissociation of H-2 in a restricted formalism. (C) 2003 Elsevier B.V. All rights reserved.