We re-examine the canonical question of Myerson and Satterthwaite (1983) whether two parties can trade an indivisible good in a Pareto efficient way when they are both privately-informed about their valuations for the good. Relaxing the assumption that utilities are quasi-linear, we show that efficient trade is generically possible if agents’ utility functions are not too responsive to private information. In natural examples efficient trade is possible even when agents’ utility functions are highly responsive to their private information. The analysis relies on new methods we introduce.