We discuss the effect of the renormalization prescription in the compu
tation of the unification point for running coupling constants. We exp
lore the effects of threshold crossing on the beta functions. We compu
te the running of the coupling constants of the Standard Model, betwee
n m(z) and Mp, using a mass-dependent subtraction procedure, and then
compare the results with ($) over bar MS, and with the theta function
approximation. We also do this for the minimal supersymmetric extensio
n of the Standard Model. In the latter, the bounds on SUSY masses that
one obtains by requiring perturbative unification are dependent, to s
ome extent, on the procedure.