--- - |2 Abstract In this paper, we develop a set‐theoretic and possible worlds approach to counterfactual analysis in case‐study explanation. Using this approach, we first consider four kinds of counterfactuals: necessary condition counterfactuals, SUIN condition counterfactuals, sufficient condition counterfactuals, and INUS condition counterfactuals. We explore the distinctive causal claims entailed in each, and conclude that necessary condition and SUIN condition counterfactuals are the most useful types for hypothesis assessment in case‐study research. We then turn attention to the development of a rigorous understanding of the ‘minimal‐rewrite’ rule, linking this rule to insights from set theory about the relative importance of necessary conditions. We show why, logically speaking, a comparative analysis of two necessary condition counterfactuals will tend to favour small events and contingent happenings. A third section then presents new tools for specifying the level of generality of the events in a counterfactual. We show why and how the goals of formulating empirically important versus empirically plausible counterfactuals stand in tension with one another. Finally, we use our framework to link counterfactual analysis to causal sequences, which in turn provides advantages for conducting counterfactual projections. - The British Journal of Sociology, EarlyView.