This study revisits the task of case selection in case study research, proposing a new typology of strategies that is explicit, disaggregated, and relatively comprehensive. A secondary goal is to explore the prospects for case selection by algorithm, aka ex ante, automatic, quantitative, systematic, or model-based case selection. We lay out a suggested protocol and then discuss its viability. Our conclusion is that it is a valuable tool in certain circumstances, but should probably not determine the final choice of cases unless the chosen sample is medium-sized. Our third goal is to discuss the viability of medium-n samples for case study research, an approach closely linked to algorithmic case selection and occasionally practiced by case study researchers. We argue that medium-n samples occupy an unstable methodological position, lacking the advantages of efficiency promised by traditional, small-n case studies but also lacking the advantages of representativeness promised by large-n samples.