  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.
