Moderate supersymmetric CP violation.

It is well known that supersymmetry (SUSY) gives neutron and electron electric dipole moments (dn and de) which are too large by about 10 . If we assume a SUSY model cannot contain fine-tunings or large mass scales, then one must require that the SUSY breaking mechanism give real soft breaking parameters, in which case the minimal SUSY model has no CP violation other than from the CKM matrix (besides possible strong CP violating effects). We show that in non-minimal SUSY models, a moderate amount of CP violation can be induced through one loop corrections to the scalar potential, giving an effective phase of order 10, and thus implying dn and de can be near their current experimental bounds naturally. This moderate amount of SUSY CP violation could also prove important for models of electroweak baryogenesis. We illustrate our results with a specific model.