We distinguish three aspects of medical diagnosis: generating new diagnostic hypotheses, selecting hypotheses for further pursuit, and evaluating their probability in light of the available evidence. Drawing on Peirce's account of abduction, we argue that hypothesis generation is amenable to normative analysis: physicians need to make good decisions about when and how to generate new diagnostic hypothesis as well as when to stop. The intertwining relationship between the generation and selection of diagnostic hypotheses is illustrated through the analysis of a detailed clinical case study. This interaction is not adequately captured by the existing probabilistic, decision-theoretic models of the threshold approach to clinical decision-making. Instead, we propose to conceptualize medical diagnosis in terms of strategic reasoning.