The surface tension of electrolyte solutions shows marked specific ion effects. We here show an important role for both ionic solvation energies and ionic dispersion potentials in determining this ion specific surface tension of salt solutions. The ion self-free energy changes when an ion moves from bulk solution into the interfacial region, with its decreasing water density profile. We will show that the solvation energies of different ions correlate very well with the surface tension of salt solutions. Inclusion of this distance-dependent self-free energy contribution brings qualitative agreement with experiments and the right Hoffmeister series. This is so not only for surface tension changes but also for measured surface potentials. The inclusion of ionic dispersion interaction potentials further improves the agreement with experiments. We discuss how further progress in the theory of the surface tension of salts can be achieved.