In supersymmetric models with complex soft breaking parameters, the CP-violating phases can filter into various sectors of the theory through loop corrections even if CP violation is absent at tree level. A notable example is the Higgs sector of the MSSM with explicit CP violation; although the phases of the soft terms and the mu parameter enter the Higgs sector only through loops, it is well known that their presence can strongly impact the physics of the Higgs sector. In this talk, I explore this phenomenon within string-motivated models with an additional U(1) gauge group broken at the TeV scale.