A central notion for allocation problems when there are private endowments is core: no coalition should be able to block the allocation. However, for an exchange economy of discrete resources, core can be empty. An alternative core-type stability axiom is the bargaining set via Aumann and Maschler (1964): a blocking by a coalition is justi ed only if there is no counter-objection to it and an allocation is in the bargaining set if there does not exist a justified blocking. We prove that the bargaining set characterizes a well-known class of trading mechanisms, the top trading cycles.