  We consider type II string compactifications on Calabi-Yau orientifolds with
fluxes and D-branes, and analyse the F-term scalar potential that
simultaneously involves closed and open string modes. In type IIA models with
D6-branes such potential can be directly computed by integrating out Minkowski
three-forms. The result shows a multi-branched structure along the space of
lifted open string moduli, in which discrete shifts in special Lagrangian and
Wilson line deformations are compensated by changes in the RR flux quanta. The
same sort of discrete shift symmetries are present in the superpotential and
constrain the Kahler potential. As for the latter, inclusion of open string
moduli breaks the factorisation between complex structure and Kahler moduli
spaces. Nevertheless, the 4d Kahler metrics display a set of interesting
relations that allow to rederive the scalar potential analytically. Similar
results hold for type IIB flux compactifications with D7-brane Wilson lines.
