Even scholars who believe the case study is a valuable research tool are skeptical that researchers can effectively generalize case findings to a wider population. However, an exception may be possible with “least likely” (LL) and “most likely” (ML) cases, often referred to as “hard” and “easy” cases, respectively. The former pose “difficult” tests of theories, in that—unlike ML cases—one would not expect a theory’s expectations to be borne out by a review of the case evidence. According to Eckstein, LL and ML cases provide researchers with a great deal of inferential leverage, being “especially tailored” to either confirming or disconfirming a theory, respectively. Such case study designs are common in the discipline of International Relations, particularly in the subfield of security studies. Since 1997, at least 36 articles appearing in Security Studies explicitly invoked the logic of LL/ML studies to justify their case selection and defend or impugn the validity of particular theories. The appeal of a study that might offer in-depth knowledge of a particular case and the generalizability of large-n cross-unit comparisons is obvious. Despite the widespread use of LL/ML cases there remains a considerable amount of imprecision regarding their definition. Researchers’ applications of the LL or ML labels typically appear plausible, but further investigation often yields uncertainty about the validity of a case’s purported difficulty. Such questions have been central to some of the most significant developments in security studies in the past two decades. For instance, the emergence of constructivist scholarship on “traditional” security issues in the 1990s had a major impact on the field, in part because such matters were alleged to be particularly hard cases for theories that privileged norms, identity, and culture to explain. However, this assertion was soon challenged by scholars who contended that constructivists studying international security had actually chosen easy cases to test their theories. This and other episodes demonstrate that the logic surrounding LL/ML cases deserves careful scrutiny, both for the sake of methodological rigor and disciplinary progress. This article addresses ambiguities surrounding LL/ML cases and provides concrete steps researchers are encouraged to follow to determine how “hard” a case is for particular theories. It uses examples from research on security matters to demonstrate how scholars can draw generalizable inferences from cases, as well as illustrate potential pitfalls researchers may confront. The first section of this article introduces the two ways scholars typically justify claims that a case is LL or ML, what I deem the “countervailing conditions” and Bayesian approaches. It briefly outlines the relationship between the two approaches, particularly focusing on the consequences of neglecting Bayesian insights when drawing inferences from case evidence. The next two sections more closely examine the core elements of the CC and Bayesian rationales, respectively, further explaining the assertions made in the first section. The necessary steps a researcher must take to determine the degree to which a case is ML or LL are also laid out in detail. The fourth section examines a study of the non-use of nuclear weapons during the Vietnam War to show how better understanding of both rationales can affect how cases are categorized and inferences reached. The article concludes by considering how LL/ML cases can contribute to research in security studies given constraints imposed by theory and evidence.