  The current experimental lower bound on the Higgs mass significantly
restricts the allowed parameter space in most realistic supersymmetric models,
with the consequence that these models exhibit significant fine-tuning. We
propose a solution to this `supersymmetric little hierarchy problem'. We
consider scenarios where the stop masses are relatively heavy - in the 500 GeV
to a TeV range. Radiative stability of the Higgs soft mass against quantum
corrections from the top quark Yukawa coupling is achieved by imposing a global
SU(3) symmetry on this interaction. This global symmetry is only approximate -
it is not respected by the gauge interactions. A subgroup of the global
symmetry is gauged by the familiar SU(2) of the Standard Model. The physical
Higgs is significantly lighter than the other scalars because it is the
pseudo-Goldstone boson associated with the breaking of this symmetry. Radiative
corrections to the Higgs potential naturally lead to the right pattern of gauge
and global symmetry breaking. We show that both the gauge and global symmetries
can be embedded into a single SU(6) grand unifying group, thereby maintaining
the prediction of gauge coupling unification. Among the firm predictions of
this class of models are new states with the quantum numbers of 10 and
$\bar{10}$ under SU(5) close to the TeV scale. The Higgs mass is expected to be
below 130 GeV, just as in the MSSM.
