  We present exact results for the spectra of three fermionic atoms in a single
well of an optical lattice. For the three lowest hyperfine states of Li6 atoms,
we find a Borromean state across the region of the distinct pairwise Feshbach
resonances. For K40 atoms, nearby Feshbach resonances are known for two of the
pairs, and a bound three-body state develops towards the positive
scattering-length side. In addition, we study the sensitivity of our results to
atomic details. The predicted few-body phenomena can be realized in optical
lattices in the limit of low tunneling.
