  We propose a model for realizing exotic paired states in cold atomic Fermi
gases. By using a {\it spin dependent} optical lattice it is possible to
engineer spatially anisotropic Fermi surfaces for each hyperfine species, that
are rotated 90 degrees with respect to one another. We consider a balanced
population of the fermions with an attractive interaction. We explore the BCS
mean field phase diagram as a function of the anisotropy, density, and
interaction strength, and find the existence of an unusual paired superfluid
state with coexisting pockets of momentum space with gapless unpaired carriers.
This state is a relative of the Sarma or breached pair states in polarized
mixtures, but in our case the Fermi gas is unpolarized. We also propose the
possible existence of an exotic paired "Cooper-pair Bose-Metal" (CPBM) phase,
which has a gap for single fermion excitations but gapless and uncondensed
"Cooper pair" excitations residing on a "Bose-surface" in momentum space.
