  We use compact D=4, N=1, Type IIB orientifolds as a testing ground for recent
ideas about precocious gauge coupling unification and a low energy string
scale. We find that certain such orientifolds have the interesting property
that gauge couplings receive moduli-dependent corrections which mimic the
effect of field theoretical logarithmic running. The effective cut-off scale
for the logarithmic correction is not $M_{string}$ but rather
$M_X=\sqrt{\alpha}M_{Planck}M_c/M_{string}$, where $M_c$ is the
compactification scale. Thus there is just normal logarithmic running up to
$M_{string}$ and extra moduli dependent corrections which behave as if there
was further running to a higher virtual scale $M_X$. In this mechanism a
prominent role is played by anomalous U(1)'s with moduli dependent
Fayet-Iliopoulos terms. A vanishing FI-term fixes the modulus dependence of the
corrected gauge coupling. We discuss possible ways to implement this mechanism
in the context of a simple extension of the MSSM.
