Because technologies and morals co-evolve, modern societies have to become adept at techno-moral learning, or the art of ‘reflective’ co-evolution. Developing this skill requires a better understanding of the various ways technology and morality challenge each other. With this aim in mind, we analyse the history of the Dutch debates on organ donation, showing how moral considerations enabled the development and application of transplantation technology. We argue that moral principles like bodily integrity and self-determination have proved to be very robust—so much so that they contribute to the scarcity of donor organs and so frustrate the full application of the transplantation technology. This ‘moral stand-still’ has led to technological experiments aimed at resolving this scarcity and to the reinterpretation of aspects of morality that seem more flexible than the principles of bodily integrity and self-determination.