  We present selected results of our program to determine the masses, gauge
couplings, and Yukawa couplings of the minimal supersymmetric model in a full
one-loop calculation. We focus on the precise prediction of the strong coupling
alpha_s(M_Z) in the context of supersymmetric unification. We discuss the
importance of including the finite corrections and demonstrate that the
leading-logarithmic approximation can significantly underestimate alpha_s(M_Z)
when some superpartner masses are light. We show that if GUT thresholds are
ignored, and the superpartner masses are less than about 500 GeV, the
prediction for alpha_s(M_Z) is quite large. We impose constraints from nucleon
decay experiments and find that minimal SU(5) GUT threshold corrections
increase alpha_s(M_Z) over most of the parameter space. We also consider the
missing-doublet SU(5) model and find that it predicts preferred values for the
strong coupling, even for a very light superpartner spectrum. We briefly
discuss predictions for the bottom-quark mass in the small tan beta region.
