Abstract When selling goods like wireless spectrum or electricity contracts, designers often opt for core-selecting mechanisms—i.e. those that induce outcomes in the core—in order to balance revenue and efficiency goals. But increasingly, auctions—such as the Federal Communications Commission’s Incentive Auction and those explored for natural resources—seek to reallocate goods, not just sell them. We show that when bidders can both buy and sell, substitutability among goods is no longer sufficient or necessary for core selection. In particular, in these environments, core selection can fail even with a single good and positive revenue, and can succeed even when some or all bidders view goods as complements. Instead, we show that the key feature that determines core selection is heterogeneity among the bidders. With too much heterogeneity, reallocation mostly realises pre-existing gains from trade among the bidders, and core selection fails. With limited heterogeneity, most gains from trade among the bidders are created by the quantity auctioned, and a core-selecting mechanism is possible.