We consider a system of dilute carriers on a lattice interacting via attractive pairwise interactions. In the regime of short coherence length the transition from superconducting to normal state does not necessarily occur through Bose decondensation into a normal fluid of pairs, as is usually assumed, but can also occur through pair unbinding. In particular, pair unbinding can dominate if the pair mobility is larger than the single-particle mobility, as occurs in models with "'off-diagonal'" interactions and in particular in the model of hole superconductivity. We discuss the interplay between pair unbinding and Bose decondensation in the dilute regime as a function of the magnitude of pair binding energy and pair mobility, and the possibility of inferring conclusions on the interactions in the microscopic Hamiltonian from observation of the various regimes. Our discussion is restricted to Hamiltonians with static interactions and valid only in the density regime where pair interactions can be ignored. Possible relevance of our results to high-To oxide superconductors is discussed.