This paper considers exchange of indivisible objects when agents are endowed with and can consume any bundles. We focus on efficient allocation rules that satisfy a novel participation requirement, the weak endowment lower bound, and which defend against simple manipulation heuristics: drop strategies and truncation strategies. Based on these properties, we obtain characterizations of a generalized version of Top Trading Cycles (TTC) on several domains. On the lexicographic and conditionally lexicographic domains, TTC is characterized by Pareto efficiency, balancedness, the weak endowment lower bound, and truncation-proofness (or drop strategy-proofness). On the domain of responsive preferences, similar characterizations are obtained by restricting attention to rules that are ``individual-good-based'' and weakening Pareto efficiency to individual-good efficiency. For the Shapley-Scarf model, TTC is characterized by Pareto efficiency, individual rationality, and truncation-proofness. The lexicographic and conditionally lexicographic domains are maximal domains on which Pareto efficiency coincides with individual-good efficiency.

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