  We study electric dipole moments (EDM) of electron and proton in
E(6)--inspired supersymmetric models with an extra U(1) invariance. Compared to
the Minimal Supersymmetric Standard Model (MSSM), in addition to offering a
natural solution to the mu problem and predicting a larger mass for the
lightest Higgs boson, these models are found to yield suppressed EDMs.
