  We construct compact type IIB orientifolds with discrete groups Z_4, Z_6,
Z_6', Z_8, Z_12 and Z_12'. These models are N=1 supersymmetric in D=4 and have
vector structure. The possibility of having vector structure in Z_N
orientifolds with even N arises due to an alternative Omega-projection in the
twisted sectors. Some of the models without vector structure are known to be
inconsistent because of uncancelled tadpoles. We show that vector structure
leads to a sign flip in the twisted Klein bottle contribution. As a
consequence, all the tadpoles can be cancelled by introducing D9-branes and
D5-branes.
