The questions tackled in this paper are: How do we deal with ethically contested medical innovations?, and Can we do better? First, I analyse how we deal with these problems by a division of labour and competitive boundary work between the medical R&D system's research and technological imperative, the medical profession's claim to self-regulation and health policy-makers' claim to political primacy and an incrementalist style of policy making. Second, turning to the normative question, I propose that policy-makers shift to a primacy of problems. Different types of problems demand different types of policy-making systems and styles. Thus, policy-makers could commence designing a health policy-making system robust enough to adequately deal with non-incremental but ethically contested medical innovations. I argue for medical innovation which also takes ethical, social and legal issues into account. This may be achieved by turning political competition through venue shopping into meta-governance through deliberate venue choice. This requires deliberative and participatory design elements in procedures and spaces for health technology assessment.