  The NAHE-set, that underlies the realistic free fermionic models, corresponds
to Z2XZ2 orbifold at an enhanced symmetry point, with (h_{11},h_{21})=(27,3).
Alternatively, a manifold with the same data is obtained by starting with a
Z2XZ2 orbifold at a generic point on the lattice and adding a freely acting Z2
involution. In this paper we study type I orientifolds on the manifolds that
underly the NAHE-based models by incorporating such freely acting shifts. We
present new models in the Type I vacuum which are modulated by Z2^n for n=2,3.
In the case of n=2, the Z2XZ2 structure is a composite orbifold Kaluza-Klein
shift arrangement. The partition function provides a simpler spectrum with
chiral matter. For n=3, the case discussed is a Z2 modulation of the T6/(Z2 X
Z2) spectrum. The additional projection shows an enhanced closed and open
sector with chiral matter. The brane stacks are correspondingly altered from
those which are present in the Z2 X Z2 orbifold. In addition, we discuss the
models arising from the open sector with and without discrete torsion.
