  We consider the ${\cal N}=1$ superpotential generated in type-II orientifold
models by non-geometric fluxes. In particular, we focus on the family of $P$
fluxes, that are related by T-duality transformations to the S-dual of the $Q$
flux. We determine the general rule that transforms a given flux in this family
under a single T-duality transformation. This rule allows to derive a complete
expression for the superpotential for both the IIA and the IIB theory for the
particular case of a $T^6/[\mathbb{Z}_2 \times \mathbb{Z}_2 ]$ orientifold. We
then consider how these fluxes modify the generalised Bianchi identities. In
particular, we derive a fully consistent set of quadratic constraints coming
from the NS-NS Bianchi identities. On the other hand, the $P$ flux Bianchi
identities induce tadpoles, and we determine a set of exotic branes that can be
consistently included in order to cancel them. This is achieved by determining
a universal transformation rule under T-duality satisfied by all the branes in
string theory.
