Symmetry-adapted perturbation theory based on Kohn-Sham determinants, SAPT(KS), was shown before to perform poorly for the electrostatic energy which is potentially exact in this approach. We demonstrate that some deficiencies of SAPT(KS) result from wrong asymptotics of exchange-correlation potentials. On applying an asymptotic correction, we were not only able to recover the electrostatics, but also the first-order exchange and second-order induction and exchange-induction energies fairly accurate. Dispersion is still reproduced poorly but can be computed reasonably accurately from the damped asymptotic expansion. (C) 2002 Published by Elsevier Science B.V.