In one of the two main theoretical approaches used in describing ultracold Fermi gases and the BEC-BCS crossover, the so-called BCS-Leggett approach, the starting point is the BCS trial wavefunction:
$$ \mid BCS \rangle \equiv \prod_{\mathbf{k}} \left( u_{\mathbf{k}} + v_{\mathbf{k}} P^\dagger_{\mathbf{k}} \right) \mid 0 \rangle $$
where the $P^\dagger_{\mathbf{k}}$ operator creates a Cooper pair. It is often asserted that this wavefunction, which may seem tailored for a BCS-like problem, has far greater validity and can also be successfully exploited in describing the BEC-BCS crossover (see for instance: http://arxiv.org/abs/cond-mat/0404274).
Even looking at the original articles by Leggett and Eagles (cited in the reference above) I cannot see why $\mid BCS \rangle$ should be valid in the BEC regime: I am looking for a review article (or even a textbook) addressing this issue.