  We study a class of superstring models compactified in the 3-generation
Calabi-Yau manifold of Tian and Yau. Our analysis includes the complete
$E_6$-singlet sector, which has been recently evaluated using techniques of
spectral and exact sequences. We use the discrete symmetries of the models to
find flat directions of symmetry breaking that leave unbroken a low energy
matter parity and make all leptoquarks heavy while preserving light Higgs
fields. Then we classify the patterns of ordinary quark mass matrices and show
that (without invoking effects due to nonrenormalizable terms) only one
structure can accommodate the observed value of fermion masses and mixing
angles, with preference for a heavy {\it top} quark ( $m_t\ge 170$ GeV for
$V_{13}\le 0.013$ ). The model, which unifies perturbatively and predicts a
realistic structure of quark mass matrices with texture zeroes, is one of the
many possible string vacua. However, in contrast with what is often assumed in
the search for realistic unified scenarios, it is highly nonminimal near the
unification scale and the predicted mass matrices have no simple symmetry
properties.
