  It is often stated in the literature concerning D=4,6 compact Type IIB
orientifolds that tadpole cancellation conditions i) uniquely fix the gauge
group (up to Wilson lines and/or moving of branes) and ii) are equivalent to
gauge anomaly cancellation. We study the relationship between tadpole and
anomaly cancellation conditions and qualify both statements. In general the
tadpole cancellation conditions imply gauge anomaly cancellation but are
stronger than the latter conditions in D=4, N=1 orientifolds. We also find that
tadpole cancellation conditions in Z_N D=4,6 compact orientifolds do not
completely fix the gauge group and we provide new solutions different from
those previously reported in the literature.
