  In order to achieve maximal stop mixing and m_h=125 GeV, we consider
extensions of minimal GMSB that include marginal MSSM-messenger superpotential
interactions. Using a new approach to analytic continuation in superspace, we
derive general formulas for the soft masses in the presence of such
interactions, correctly taking into account the role of MSSM-messenger mixing
in a general framework for the first time. We classify and catalog all possible
such interactions consistent with perturbative SU(5) unification, and we survey
the impact of turning on one interaction at a time, from the point of view of
fine tuning, spectrum and phenomenology. We find that the best models are
fine-tuned to the sub-percent level and are accessible at the 14 TeV LHC. We
highlight potential search strategies that can probe the characteristic spectra
of these models.
