Using periodic density-functional theory calculations, we address the work-function change induced by the adsorption of chlorine and iodine on Cu(111) which are shown to change the work function in opposite ways, contrary to what one may expect for these two electron acceptors. In contrast to previous studies, we demonstrate that substrate effects play only a minor role in work-function changes brought about by halogen adsorption on metals. Instead, polarization on the adsorbate not only explains the sign of the work-function change as a contributor to a positive surface dipole moment, but it is also the decisive factor in the dependence of adsorption-induced work-function changes on the coverage of halogens on metal surfaces.