We study the influence of the phonon spectrum on polaron formation and show that three self-trapping regimes can occur. If the lattice and the electron-lattice Hamiltonians are dominated by the same type of phonons, the self-trapping transition is smooth. If there is an imbalance, the transition can either be abrupt or completely eliminated. The binding energies are larger in the case of imbalance. The bandwidth varies linearly with hopping strength, even for strongly localized states. (C) 2000 Elsevier Science B.V.