  We construct a class of geometric twists of Calabi-Yau manifolds of
Voisin-Borcea type (K3 x T^2)/Z_2 and study the superpotential in a type IIA
orientifold based on this geometry. The twists modify the direct product by
fibering the K3 over T^2 while preserving the Z_2 involution. As an important
application, the Voisin-Borcea class contains T^6/(Z_2 x Z_2), the usual
setting for intersecting D6 brane model building. Past work in this context
considered only those twists inherited from T^6, but our work extends these
twists to a subset of the blow-up modes. Our work naturally generalizes to
arbitrary K3 fibered Calabi-Yau manifolds and to nongeometric constructions.
