The newest convention of the Council of Europe requires states parties to criminalize all activities related to the trafficking in human organs. It is the first international agreement specifically aimed at addressing this form or criminal trade. Trafficking in human organs is mostly a transnational criminal enterprise: the article highlights how contracting states will have to face specific problems in prosecuting offences committed in foreign countries. The effectiveness of the convention depends on the parties’ determination in solving such problems and in avoiding taking advantage from some reservations that – though admitted by the convention – could undermine its possible value as a means of combating transnational crime.