  We study the effective action of the heterotic string compactified on
particular half-flat manifolds which arise in the context of mirror symmetry
with NS-NS flux. We explicitly derive the superpotential and Kahler potential
at lowest order in alpha' by a reduction of the bosonic action. The
superpotential contains new terms depending on the Kahler moduli which
originate from the intrinsic geometrical flux of the half-flat manifolds. A
generalized Gukov formula, valid for all manifolds with SU(3) structure, is
derived from the gravitino mass term. For the half-flat manifolds it leads to a
superpotential in agreement with our explicit bosonic calculation. We also
discuss the inclusion of gauge fields.
