  In a recent paper, we proposed the possibility that supersymmetry breaking is
communicated dominantly via a U(1)' vector multiplet. We also required that the
U(1)' plays a crucial role in solving the mu problem. We discuss here in detail
both the construction and the phenomenology of one class of such models. The
low energy spectrum generically contains heavy sfermions, Higgsinos and exotics
~10-100 TeV; an intermediate M_Z' ~ 3-30 TeV; light gauginos ~100-1000 GeV, of
which the lightest can be wino-like; a light Higgs with a mass of ~140 GeV; and
a singlino which can be very light. We present a set of possible consistent
charge choices. Several benchmark models are used to demonstrate characteristic
phenomenological features. Special attention is devoted to interesting LHC
signatures such as gluino decay and the decay patterns of the electroweak-inos.
Implications for neutrino masses, exotic decays, R-parity, gauge unification,
and the gravitino mass are briefly discussed.
