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 _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.