Osmotic coefficients of a series of 16 aqueous electrolyte solutions are described at concentrations up to about 1 M with the help of HNC calculations and solvent-averaged potentials of charged hard spheres with an additional necessary dispersion potential, omitted from all earlier treatments. The adjusted ionic radii and excess polarizabilities have values of the expected order of magnitude. Whereas the description of the bulk properties is satisfactory, the theory is not so successful in predicting the surface tensions of the corresponding solutions (Hofmeister series). The reasons for this are quite subtle and explored in the text. It is clear now how to make further progress and tackle hydration in a consistent way.