Research on graphical methods of reasoning has made enormous progress since the pioneering work of Wigmore in the early 20th century and its later rediscovery in the 1980s. While the usefulness of graphical methods for student training and research is widely acknowledged, their use by judges remains marginal, if not non-existent, even though this was Wigmore's objective. This article explores the difficulties that graphical methods of reasoning must overcome if they are to be integrated into the practice of the courts, at a time when courts are faced with ever more pressing imperatives of efficiency. The research is based on a partnership with the French School of Magistrates (Ecole Nationale de la Magistrature) and is informed by training courses given to magistrates on the basis of real cases, during which the authors proposed that they implement what we have called the Orderly Method of Evidence Analysis. Although the research confirms the value of graphical methods in promoting rigour in evidential reasoning, it also reaffirms the already clearly identified limits related to their complexity and time-consuming nature. The article also points out the difficulties that still need to be overcome in order to operationalise graphical methods of evidential reasoning, and the difficulties encountered by these methods in avoiding judgment bias.