  We study supersymmetric orientifolds where the world-sheet parity
transformation is combined with a conjugation of some compact complex
coordinates. We investigate their T-duality relation to standard orientifolds
and discuss the origin of continuous and discrete moduli. In contrast to
standard orientifolds, the antisymmetric tensor describes a continuous
deformation, while the off-diagonal part of the metric is frozen to quantized
values and is responsible for the rank reduction of the gauge group. We also
give a geometrical interpretation of some recently constructed six-dimensional
permutational orientifolds.
