  We study the evolution of the gauge coupling constants in string unification
schemes in which the light spectrum below the compactification scale is exactly
that of the minimal supersymmetric standard model. In the absence of string
threshold corrections the predicted values $\sin^2\theta _W=0.218$ and $\alpha
_s=0.20$ are in gross conflict with experiment, but these corrections are
generically important. One can express the string threshold corrections to
$\sin^2\theta _W$ and $\alpha_s$ in terms of certain $modular$ $weights$ of
quark, lepton and Higgs superfields as well as the $moduli$ of the string
model. We find that in order to get agreement with the experimental
measurements within the context of this $minimal$ scheme, certain constraints
on the $modular$ $weights$ of the quark, lepton and Higgs superfields should be
obeyed. Our analysis indicates that this $minimal$ $string$ $unification$
