  There are few robust solutions to the doublet-triplet splitting problem in
supersymmetric GUT theories. One of the more promising solutions is the Higgs
as pseudo-Goldstone boson mechanism. In its minimal implementation, such a
solution places an additional restriction on the parameter space of the minimal
supersymmetric standard model. A testable consequence of this constraint is an
equation for $\tan \beta$. We present this restriction and study its solutions
in order to constrain the allowed parameter space. Thus the assumptions on the
GUT scale Higgs sector should yield testable predictions for weak scale
physics. If the SUSY parameters are measured then it should be possible to
check the predictions, yielding insight into GUT scale physics.
