The self-consistent density-functional formalism has been used to calculate electronic densities around light interstitial impurities in jellium. The resulting charge densities have been fitted to a simple analytic expression and the fit parameters determined as functions of rs for all metallic densities. Energy profiles have then been calculated in 17 simple metals with the use of up to six different local pseudopotentials in first-order perturbation theory. The dependence of the energy on the choice of pseudopotential is discussed. In some cases it was possible to predict the stable interstitial site and the most probable diffusion paths. The zero-point energy of positive muons and protons in the calculated potentials has been estimated and the problem of localization discussed. The effect of the zero-point motion of the lattice ions is shown to be negligible. The modification of the energy profiles with lattice relaxation has been studied in the case of Al.