  We consider spin-polarized mixtures of cold fermionic atoms on the BEC side
of the Feshbach resonance. We demonstrate that a strongly anisotropic confining
potential can give rise to a double-peak structure in the axial distribution of
the density difference and a polarization-dependent aspect ratio of the
minority species. Both phenomena appear as a result of the breakdown of the
local density approximation for the phase-separated regime. We speculate on the
implications of our findings for the unitary regime.
