We study the effect of integrating out the heavy modes on an effective theory obtained by compactification of the heterotic string. We argue that this integration is possible in principle under two basic assumptions: (i) the underlying string theory is finite, and (ii) supersymmetry is not broken through compactification. We illustrate this method on a specific example where enough can be inferred about the details of the couplings of the heavy fields to perform the explicit calculation, and we show that the leading N (number of chiral supermultiplets) contributions quadratic in the compactification scale can be absorbed into a redefinition of the Kähler potential. This redefinition amounts to adding a ``Casimir energy'' type term to the Kähler potential. We use the prescription of Dine, Rohm, Seiberg and Witten to obtain the corresponding one-loop corrections to the effective theory below the scale of hidden gaugino condensation. These corrections do not lift the ground state degeneracy of the potential of Dine et al., and make no contribution to observable soft supersymmetry breaking effects, in agreement with a previous conjecture.