Exploring informal components of clinical reasoning, we argue that they need to be understood via the analysis of professional wisdom. Wise decisions are needed where action or insight is vital, but neither everyday nor expert knowledge provides solutions. Wisdom combines experiential, intellectual, ethical, emotional and practical capacities; we contend that it is also more strongly social than is usually appreciated. But many accounts of reasoning specifically rule out such features as irrational. Seeking to illuminate how wisdom operates, we therefore build on Aristotle's work on informal reasoning. His account of rhetorical communication shows how non-formal components can play active parts in reasoning, retaining, or even enhancing its reasonableness. We extend this account, applying it to forms of healthcare-related reasoning which are characterised by the need for wise decision-making. We then go on to explore some of what clinical wise reasoning may mean, concluding with a case taken from psychotherapeutic practice.