  We study the breaking of supersymmetry in models with anomalous U(1). These
models are simple to construct and contain natural candidates for being the
messengers of gauge-mediated supersymmetry breaking. When some of the ordinary
matter fields transform under the anomalous U(1), we find a hybrid scenario in
which the U(1) and the gauge interactions mediate the breaking of
supersymmetry. This leads to a hierarchy of soft masses between the charged and
neutral fields and provides a solution to the $\mu$-problem. Among these
models, we present a scenario in which the Higgs arises as a pseudo-Goldstone
boson. This scenario naturally allows for values of the $\mu$-term and the
scalar soft masses larger than the weak scale.
