Concrete non trivial computation of Morse homology

Question

I am studying Morse homology and have found only examples on spheres and tori so far. Of course the homology of these manifolds is better understood by other more standard methods, so I am having difficulties understanding what is the gain of this homology theory. I know there is some kind of "conceptual" gain in this approach to homology, since it leads to some useful generalization to the infinite-dimensional case. Anyway, I would like to see some finite dimensional example in which the construction of the Morse-Smale-Witten complex is actually easier (or more natural, in any sense) then "classical algebraic-topological methods".