Open descendants of Z₂ × Z₂ freely acting orbifolds

We discuss Z₂ × Z₂ 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 → N = 1, N = 4 → N= 1 and N = 4 → 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.