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We provide epistemic foundations for permissibility (Brandenburger, 1992), a strategic-form solution concept for finite games which coincides with the Dekel-Fudenberg procedure, i.e., the elimination of all weakly dominated strategies, followed by the iterated elimination of strictly dominated strategies. We show that permissibility characterizes the behavioral implications of “cautious rationality and common weak belief of cautious rationality” in the canonical, universal type structure for lexicographic beliefs. For arbitrary type structures, we show that the behavioral implications of these epistemic assumptions are characterized by the solution concept of full weak best response set, a weak dominance analogue of best response set (Pearce, 1984).