This article maps the elements of the epistemically legitimate argumentative space of judges in scientific disputes, where scientific facts and arguments intrude into the legally relevant aspects of the legal controversy. The article distinguishes four main forms of legitimate hybrid reasoning styles. It identifies the epistemic risks threatening the legitimacy of decisions in light of the corresponding limits of the epistemically legitimate argumentative space. The article concludes by discussing the parameters which help judges to select the appropriate reasoning style in particular cases, such as the judicial institution’s epistemic capacities, practical feasibility, and the role science plays in the fabric of legal rules.