  We revisit an extension of the MSSM by adding a hypercharge-neutral,
SU(2)-triplet chiral superfield. Similar to the NMSSM, the triplet gives an
additional contribution to the quartic coupling in the Higgs potential, and the
mass of the lightest CP-even Higgs boson can be greater than tne mass of the
Z-bosn at tree-level. In addition to discussing the perturbativity,
fine-tuning, and decoupling issues of this model, we compute the dominant
1-loop corrections to the mass of the lightest CP-even Higgs boson from the
triplet sector. When the Higgs-Higgs-Triplet coupling in the superpotential is
comparable to the top Yukawa coupling, we find that the Higgs mass can be as
heavy as 140 GeV even without the traditional contributions from the top--s-top
sector, and at the same time consistent with the precision electroweak
constraints. At the expense of having Landau poles before the GUT scale, this
opens up a previously forbidden region in the MSSM parameter space where both
s-tops are light. In addition to having relatively small fine-tuning (about one
part in 30), this leads to a gluo-philic Higgs boson whose production via
gluon-gluon fusion at the LHC can be twice as large as the SM prediction.
