  We discuss the calculation of threshold corrections to gauge coupling
constants for the, only, non-decomposable class of abelian (2, 2) symmetric N=1
four dimensional heterotic orbifold models, where the internal twist is
realized as a generalized Coxeter automorphism. The latter orbifold was singled
out in earlier work as the only N=1 heterotic $Z_N$ orbifold that satisfy the
phenomenological criteria of correct minimal gauge coupling unification and
cancellation of target space modular anomalies.
