  The four-dimensional effective theory for type IIB warped flux
compactifications proposed in [1] is completed by taking into account the
backreaction of the K\"ahler moduli on the three-form fluxes. The only required
modification consists in a flux-dependent contribution to the chiral fields
parametrising the K\"ahler moduli. The resulting supersymmetric effective
theory satisfies the no-scale condition and consistently combines previous
partial results present in the literature. Similar results hold for M-theory
warped compactifications on Calabi-Yau fourfolds, whose effective field theory
and K\"ahler potential are also discussed.
