  Quasi--realistic heterotic-string models in the free fermionic formulation
typically contain an anomalous U(1), which gives rise to a Fayet-Iliopolous
term that breaks supersymmetry at the one--loop level in string perturbation
theory. Supersymmetry is restored by imposing F- and D-flatness on the vacuum.
In Phys. Rev. D 78 (2008) 046009, we presented a three generation free
fermionic standard-like model which did not admit stringent F- and D-flat
directions, and argued that the all the moduli in the model are fixed. The
particular property of the model was the reduction of the untwisted Higgs
spectrum by a combination of symmetric and asymmetric boundary conditions with
respect to the internal fermions associated with the compactified dimensions.
In this paper we extend the analysis of free fermionic models with reduced
Higgs spectrum to the cases in which the SO(10) symmetry is left unbroken, or
is reduced to the flipped SU(5) subgroup. We show that all the models that we
study in this paper do admit stringent flat directions. The only examples of
models that do not admit stringent flat directions remain the strandard-like
models of reference Phys. Rev. D 78 (2008) 046009.
