In an earlier report the van der Waals interaction between an atom and a metal surface was calculated taking into account the finite extension of the atom. This was found to make the atom to response less well to density fluctuations of short wavelengths. Since those fluctuations are more important close to the surface, the ordinary divergent expression for the van der Waals potential, when the atom-metal separation goes to zero, was replaced by another which gave finite values of the interaction even at distances very close to the surface. The previous treatment is extended in this paper to include also the inability of the metal itself to respond to short wavelength density fluctuations. As can be expected, the improved metal response affects the physisorption potential close to the surface. Oure results are conveniently parameterized for a number of atom/metal configurations in order to make them of easy use in many other applications.