  Anomaly mediation solves the supersymmetric flavor and CP problems. This is
because the superconformal anomaly dictates that supersymmetry breaking is
transmitted through nearly flavor-blind infrared physics that is highly
predictive and UV insensitive. Slepton mass squareds, however, are predicted to
be negative. This can be solved by adding D-terms for U(1)_Y and U(1)_{B-L}
while retaining the UV insensitivity. In this paper we consider electroweak
symmetry breaking via UV insensitive anomaly mediation in several models. For
the MSSM we find a stable vacuum when tanbeta < 1, but in this region the top
Yukawa coupling blows up only slightly above the supersymmetry breaking scale.
For the NMSSM, we find a stable electroweak breaking vacuum but with a chargino
that is too light. Replacing the cubic singlet term in the NMSSM superpotential
with a term linear in the singlet we find a stable vacuum and viable spectrum.
Most of the parameter region with correct vacua requires a large superpotential
coupling, precisely what is expected in the ``Fat Higgs'' model in which the
superpotential is generated dynamically. We have therefore found the first
viable UV complete, UV insensitive supersymmetry breaking model that solves the
flavor and CP problems automatically: the Fat Higgs model with UV insensitive
anomaly mediation. Moreover, the cosmological gravitino problem is naturally
solved, opening up the possibility of realistic thermal leptogenesis.
