The English National Health Service Constitution states that patients have the right to expect all decisions about access to medicines and treatments to be made ‘rationally’. Rationality in health care can be framed as instrumental, institutional or practical. In this article, we present a case example from an ethnographic study of the work of ‘Individual Funding Request’ panels to explore how rationality is enacted and accounted for in deliberations about the rationing of health care in the National Health Service. Our rhetorical analysis highlights how an embodied, practical rationality emerges as a significant aspect of rationality in practice, but at the same time has a problematic status in formal accounts of decision-making. We suggest that being both ‘human’ and ‘rational’ is a ‘delicate balance’ and creates a dilemma for Individual Funding Request panels. Aristotle’s notion of phronesis provides a useful lens for theorising our observation of panel deliberations, and we argue for greater attention to the value of narrative ethics in helping us understand the challenges faced by resource allocators.