  We consider supersymmetry breaking in theories with gaugino condensation in
the presence of an anomalous U(1) symmetry with anomaly cancellation by the
Green-Schwarz mechanism. In these models, a Fayet-Iliopoulos D-term can give
important contributions to the soft supersymmetry-breaking scalar masses. Most
discussions of this possibility have ignored the dilaton field. We argue that
this is not appropriate in general, and show that the F-term contributions to
the soft breaking terms are comparable to or much larger than the D-term
contributions, depending on how the dilaton is stabilized. We discuss
phenomenological implications of these results.
