  We propose a simple gauge extension of the minimal supersymmetric standard
model (MSSM), where the fine tuning in the Higgs mass parameters is highly
reduced. The Higgs boson is insensitive to high energies because of
supersymmetry and also because it is a pseudo-Goldstone boson of a global
symmetry (referred to as double protection or super-little Higgs mechanism). A
large shift in the Higgs quartic self coupling is obtained via a non-decoupling
D-term coming from an extra gauge group, resulting in a Higgs that can be as
heavy as 135 GeV with a tuning milder than 10%. With an appropriate choice of
quantum numbers one can achieve that the additional quartic is generated
without a corresponding shift in the Higgs mass, thus preserving the double
protection of the Higgs. The model predicts the existence of several
top-partner fermions one of which can be as light as 700 GeV, while the
ordinary MSSM states could be as light as 400 GeV. In addition to many new
particles in the multi-TeV range there would also be an axion-like state very
weakly coupled to standard model (SM) matter which could be in the sub-GeV
regime, and sterile neutrinos which could be light.
