To advocates of QCA, this methodology represents a valuable middle-ground between the limitations of both small-n case study research and large-n statistical analysis.   QCA claims to borrow the best of both (methodological) worlds without falling victim to either of their shortcomings.  In principle, this approach encompasses the depth of case studies and the rigor of statistics.  Correspondingly, practitioners of QCA make broad and impressive claims about the extent to which QCA improves upon existing methodologies as well as the unique contributions it provides to causal inference. This methodology, however, is founded on a number of problematic assumptions; and its implementation relies on practices that raise even greater concern. This paper summarizes and evaluates a series of specific claims made by QCA as a basis for evaluating both its theoretical and practical utility.  I show that while it makes genuine contributions, a wide gap exists between what advocates claim to infer from it and the insights it actually yields.  This paper concludes by underscoring the need for further methodological work on tools for medium-N analysis.