Societies prohibit many transactions considered morally repugnant, although potentially efficiency-enhancing. We conducted an online choice experiment to characterize preferences for the morality and efficiency of payments to kidney donors. Preferences were heterogeneous, ranging from deontological to strongly consequentialist; the median respondent would support payments by a public agency if they increased the annual kidney supply by six percentage points, and private transactions for a thirty percentage-point increase. Fairness concerns drive this difference. Our findings suggest that cost-benefit considerations affect the acceptance of morally controversial transactions, and imply that trial studies of the effects of payments would inform the public debate.