We examine the behavior of the superconducting order parameter near a superconductor-insulator interface by self-consistently solving the Gor'kov equations in a slab geometry. We obtain results as a function of temperature and the coherence length ξ 0 . We find that even for small values of ξ 0 there is no significant depletion of the gap parameter near such an interface over any extended temperature range. This is in agreement with experimental information and in contrast with results obtained from an extrapolation of standard Ginzburg-Landau based results. We also find that quantum-size effects, which are present in the large ξ 0 case, disappear as ξ 0 decreases