  We present a new approach to the mu-Bmu problem of gauge mediated
supersymmetry breaking. Rather than reducing the generically large contribution
to Bmu we point out that acceptable electroweak symmetry breaking can be
achieved with mu^2 << Bmu if at the same time Bmu << m_Hd^2. This hierarchy can
easily appear in models where the Higgs fields are directly coupled to the
supersymmetry breaking sector. Such models can yield novel electroweak symmetry
breaking vacua, can deal with the supersymmetric flavor and CP problems, allow
for gauge coupling unification, and result in distinct phenomenological
predictions for the spectrum of superparticles.
