  We discuss Z_2 \times Z_2 orientifolds where the orbifold twists are
accompanied by shifts on momentum or winding lattice states. The models contain
variable numbers of D5 branes, whose massless (and, at times, even massive)
modes have variable numbers of supersymmetries. We display new type-I models
with partial supersymmetry breaking N=2 \to N=1, N=4 \to N=1 and N=4 \to N=2.
The geometry of these models is rather rich: the shift operations create brane
multiplets related by orbifold transformations that support gauge groups of
reduced rank. Some of the models are deformations of six-dimensional
supersymmetric type-I models, while others have dual M-theory descriptions.
