Causal inference via process tracing has received increasing attention during recent years. A 2 x 2 typology of hypothesis tests takes a central place in this debate. A discussion of the typology demonstrates that its role for causal inference can be improved further in three respects. First, the aim of this article is to formulate case selection principles for each of the four tests. Second, in focusing on the dimension of uniqueness of the 2 x 2 typology, I show that it is important to distinguish between theoretical and empirical uniqueness when choosing cases and generating inferences via process tracing. Third, I demonstrate that the standard reading of the so-called doubly decisive test is misleading. It conflates unique implications of a hypothesis with contradictory implications between one hypothesis and another. In order to remedy the current ambiguity of the dimension of uniqueness, I propose an expanded typology of hypothesis tests that is constituted by three dimensions.