In the gauge-mediation framework the soft supersymmetry breaking mass param
eters of the supersymmetric standard model are induced by the gauge interac
tions of some messenger fields. The parameters exhibit flavor universality
which is dictated by the gauge interactions and which efficiently eliminate
s new dangerous contributions to flavor changing neutral currents. However,
the Higgs potential in this framework typically contains an unacceptable h
ierarchy between its dimensionful parameters (the mu problem of gauge media
tion). We show that the problem can be resolved if the Higgs potential aris
es dynamically once an intermediate U(1)' sector is integrated out rather t
han arising radiatively from some Yukawa interactions at the messenger scal
e. As an added benefit, such models may naturally avoid new contributions t
o CP violating amplitudes. The proposed framework is described, explicit ex
amples are given and its phenomenology is explored. The mu problem is resol
ved in this case by the low-energy U(1)' dynamics which could be tested in
future collider experiments. [S0556-2821(99)08019-4].