  Fibrations of flux backgrounds by supersymmetric cycles are investigated. For
an internal six-manifold M with static SU(2) structure and mirror \hat{M}, it
is argued that the product M x \hat{M} is doubly fibered by supersymmetric
three-tori, with both sets of fibers transverse to M and \hat{M}. The mirror
map is then realized by T-dualizing the fibers. Mirror-symmetric properties of
the fluxes, both geometric and non-geometric, are shown to agree with previous
conjectures based on the requirement of mirror symmetry for Killing
prepotentials. The fibers are conjectured to be destabilized by fluxes on
generic SU(3)xSU(3) backgrounds, though they may survive at type-jumping
points. T-dualizing the surviving fibers ensures the exchange of pure spinors
under mirror symmetry.
