Type-IIB orientifolds without untwisted tadpoles, and non-BPS D-branes

We discuss the construction of six- and four-dimensional type-IIB orientifo lds with vanishing untwisted RR tadpoles, but generically non-zero twisted RR tadpoles. Tadpole cancellation requires the introduction of D-brane syst ems with zero untwisted RR charge, but non-zero twisted RR charges. We cons truct explicit models containing branes and antibranes at fixed points of t he internal space, or non-BPS branes partially wrapped on it. The models ar e non-supersymmetric, but are absolutely stable against decay to supersymme tric vacua. For particular values of the compactification radii tachyonic m odes may develop, triggering phase transitions between the different types of non-BPS configurations of branes, which we study in detail in a particul ar example. As an interesting spin-off, we show that the T-6/Z(4) orientifo ld without vector structure, previously considered inconsistent due to unca ncelable twisted tadpoles, can actually be made consistent by introducing a set of brane-antibrane pairs whose twisted charge cancels the problematic tadpole.