  Standard results in 4d N=1 string compactifications assign a number of moduli
to each space-time filling D-brane, computed by analysing the D-brane action in
a fixed background. We revisit such conventional wisdom and argue that this
naive counting of open string moduli is incorrect, in the sense that some of
them will be lifted when making dynamical the bulk degrees of freedom. We
explicitly discuss this effect for D6-branes wrapping special Lagrangian
three-cycles, showing that some geometric and Wilson line moduli are lifted
even before taking into account worldsheet instanton effects. From a 4d
effective theory viewpoint the moduli lifting is due to an F-term potential,
and can be deduced from the superpotentials in the literature. From a
microscopic viewpoint the lifting is due to D-brane backreaction effects and
flux quantisation in a compact manifold, and provides a mechanism for lifting
Wilson line moduli. The latter applies to certain D6-branes and D7-brane Wilson
lines, yielding new possibilities to build models of inflation in string
theory.
