Recent research shows that properly devised economic incentives increase the supply of blood without hampering its safety; similar effects may be expected also for other body parts such as bone marrow and organs. These positive effects alone, however, do not necessarily justify the introduction of payments for supplying body parts; these activities concern contested commodities or repugnant transactions, i.e. societies may want to prevent certain ways to regulate a transaction even if they increased supply, because of ethical concerns. When transactions concern contested commodities, therefore, societies often face trade-offs between the efficiency-enhancing effects of trades mediated by a monetary price, and the moral opposition to the provision of these payments. In this essay, I first describe and discuss the current debate on the role of moral repugnance in controversial markets, with a focus on markets for organs, tissues, blood and plasma. I then report on recent research focused on understanding the trade-offs that individuals face when forming their opinions about how a society should organize certain transactions.