We show that the incentive to engage in exclusionary tying (of two complementary products) may arise even when tying cannot be used as a defensive strategy to protect the incumbent’s dominant position in the primary market. By engaging in tying, an incumbent firm sacrifices current profits but can exclude a more efficient rival from a complementary market by depriving it of the critical scale it needs to be successful. In turn, exclusion in the complementary market allows the incumbent to be in a favourable position when a more efficient rival will enter the primary market, and to appropriate some of the rival’s efficiency rents. The paper also shows that tying is a more profitable exclusionary strategy than pure bundling, and that exclusion is the less likely the higher the proportion of consumers who multi-home.