  It is well known that supersymmetry (SUSY) gives neutron and electron
electric dipole moments ($d_n$ and $d_e$) which are too large by about
$10^{3}$. 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 $10^{-3}$, and thus implying $d_n$ and $d_e$
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.
