  We propose a framework for natural breaking of electroweak symmetry in
supersymmetric models, where elementary Higgs fields are semi-perturbatively
coupled to a strong superconformal sector. The Higgs VEVs break conformal
symmetry in the strong sector at the TeV scale, and the strong sector in turn
gives important contributions to the Higgs potential, giving rise to a kind of
Higgs bootstrap. A Higgs with mass $125\GeV$ can be accommodated without any
fine tuning. A Higgsino mass of order the Higgs mass is also dynamically
generated in these models. The masses in the strong sector generically violate
custodial symmetry, and a good precision electroweak fit requires tuning of
order $\sim 10%$. The strong sector has an approximately supersymmetric
spectrum of hadrons at the TeV scale that can be observed by looking for a peak
in the $WZ$ invariant mass distribution, as well as final states containing
multiple $W$, $Z$, and Higgs bosons. The models also generically predict large
corrections (either enhancement or suppression) to the $h \to \ga\ga$ width.
