Two assumptions are used to justify selection of equilibria in stable sets. One assumption requires that a selected set is invariant to addition of redundant strategies. The other is a strong version of backward induction. Backward induction is interpreted as the requirement that behavior strategies in an extensive-form game are sequentially rational and conditionally admissible at every information set; viz., quasi-perfect as defined by van Damme. The strong version requires truly quasi-perfect, in that every action perturbation selects a quasi-perfect equilibrium in the set. For two-player games we also provide an exact characterization of stable sets.