Supersymmetric b-tau unification, gauge unification, and fixed points

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 greater than or similar to 10% in the gauge coupling unification assumption (which necessarily implies large perturbations at the grand scale). The constraints are shown to diminish:ln that case [most significantly so if alpha(s)(M(Z)) approximate to 0.11]. In particular, the requirement that the t Yukawa coupling h(t) is near its quasifixed 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, 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.