In density-functional theory, the standard Perdew-Zunger method of self-int
eraction correction leads to exchange-correlation (xc) potentials that are
orbital-dependent. We study various simplified implementations of self-inte
raction correction-derived in the framework of the so-called optimized effe
ctive potential method-that lead to a single, orbital-independent re potent
ial. The performance of the various self-interaction corrected functionals
is tested for sodium clusters: we first consider a variety of ground-state
properties (total energies, Kohn-Sham orbital eigenvalues, and ionic potent
ial curves) and then study the dynamical regime of weak and strong electron
ic excitations. It turns out that for sodium clusters the simplest, global-
averaging scheme gives a good description of static and dynamic properties,
even in the regime of strong excitations.