  A 125 GeV Higgs renders the simpler GMSB models unnatural, essentially
pushing the soft spectrum beyond the LHC reach. A direct coupling of the matter
and messenger fields, that facilitates an enhanced mixing in the squark sector,
is a way to ameliorate this deficiency. We construct all possible
messenger-matter interaction terms considering the messenger multiplets in 1, 5
and 10 dimensional representations of the SU(5). A Froggatt-Nielsen like flavor
framework connected with the origin of fermion mass hierarchy is utilized to
control the interaction terms and suppress FCNC. We perform a detailed
comparative study of the efficiency of such interaction terms to boost the
Higgs mass keeping the soft spectrum light. We identify the more promising
models and comment on their status in present and future collider studies.
