Challenging the contention that statistical methods applied to large numbers of cases invariably provide better grounds for causal inference, this article explores the value of a method of systematic process analysis that can be applied in a small number of cases. It distinguishes among three modes of explanation - historically specific, multivariate, and theory-oriented - and argues that systematic process analysis has special value for developing theory-oriented explanations. It outlines the steps required to perform such analysis well and illustrates them with reference to Owen's investigation of the 'democratic peace'. Comparing the results available from this kind of method with those from statistical analysis, it examines the conditions under which each method is warranted. Against conceptions of the 'comparative method' which imply that small-n case-studies provide weak grounds for causal inference, it argues that the intensive examination of a small number of cases can be an appropriate research design for testing such inferences.