Recent high-precision experimental results for photon scattering from neon $(\ensuremath{\approx}1%$ accuracy) have indicated that even present sophisticated S-matrix results are not sufficient to obtain agreement, even though the photon energies involved were many times the innermost threshold energy. In this case the discrepancy was traced to the use of local exchange and the neglect of electron-correlation effects. Here we present a general scheme for applying corrections to the S-matrix results to account for nonlocal-exchange effects and electron-correlation effects, so as to obtain results expected to be accurate at the 1% level in all elements for such energies. The corrections are based on results in simpler approximations: the form-factor approximation for elastic Rayleigh scattering, and the impulse and incoherent-scattering-factor approximations for inelastic Compton scattering. The case of scattering from neon is investigated in detail for all scattering angles and for photon energies in the range 1--100 keV. The scheme breaks down below $\ensuremath{\approx}1 \mathrm{keV}$ for elastic scattering and at low momentum transfers for inelastic scattering. We also discuss the validity of the simpler approximations, particularly the use of the impulse approximation in describing Compton scattering.