  The equality assumption of the b and tau Yukawa couplings at the
grand-unification scale can strongly constrain the allowed parameter space of
supersymmetric models. We examine the constraints in the case that there is a
discrepancy > 10% in the gauge coupling unification assumption (which
necessarily implies large perturbations at the grand scale). The constraints
are shown to diminish in that case [most significantly so if alpha_{s}(M_{Z})
\approx 0.11]. In particular, the requirement that the t Yukawa coupling,
h_{t}, is near its quasi-fixed point may not be necessary. We discuss the
colored-triplet threshold as a simple example of a source for the
discrepancies, and comment on its possible implications. In addition, we point
out that supersymmetric (as well as unification-scale) threshold corrections to
h_{t} shift the fixed-point curve in the m_{t} - \tan\beta plane. The
implications for the prediction of the Higgs boson mass are briefly discussed.
