We compute the full set of weak-scale gauge and Yukawa threshold corre
ctions in the minimal supersymmetric standard model, including ah fini
te (non-logarithmic) corrections, which we show to be important. We us
e our results to examine the effects of unification-scale threshold co
rrections in the minimal and missing-doubler SU(5) models. We work in
the context of a unified mass spectrum, with scalar mass M(0) and gaug
ino mass M(1/2), and find that in minimal SU(5) with squark masses les
s than one TeV, successful gauge and Yukawa coupling unification requi
res M(1/2) << M(0) and M(0) similar or equal to 1 TeV. In contrast, we
find that the missing-doubler model permits gauge and Yukawa unificat
ion for a wide range of supersymmetric masses.