  We present a simple model that achieves $m_h\approx 126$ GeV in the MSSM with
large $A$-terms and TeV-scale stops through a combination of gauge mediation
and Higgs-messenger interactions. The $\mu$/$B_\mu$ and $A$/$m_H^2$ problems
are both solved by a common mechanism -- partial sequestering from strong
hidden sector dynamics. Using the framework of General Messenger Higgs
Mediation, we explicitly calculate the soft masses in terms of the vacuum
expectation values, operator dimensions and OPE coefficients of the
strongly-coupled hidden sector. Along the way, we also present a general
analysis of the various constraints on sequestered Higgs mediation models. The
phenomenology of such models is similar to gaugino mediation, but with large
$A$-terms. The NLSP is always long-lived and is either the lightest stau or the
Higgsino. The colored states are typically out of reach of the 8 TeV LHC, but
may be accessible at 14 TeV, especially if the NLSP is the lightest stau.
