Spontaneous CP Violation in Models with Anomalous U(1)

We examine a class of Froggatt-Nielsen models with an anomalous U(1) as the flavor dependent symmetry. Anomaly cancellation and unbroken supersymmetry impose constraints on the U(1)_X charges of the fermions and the vacuum expectation values of the symmetry-breaking scalars. We show by example that it is possible to find models that reproduce the observed masses and mixings of the standard model fermions, and exhibit a realistic amount of CP violation.