In this paper, we first briefly survey the main responses to the challenge that experimental philosophy poses to the method of cases, given the common assumption that the latter is crucially based on intuitive judgments about cases. Second, we discuss two of the most popular responses in more detail: the expertise defense and the mischaracterization objection. Our take on the expertise defense is that the available empirical data do not support the claim that professional philosophers enjoy relevant expertise in their intuitive judgments about cases. In contrast, the mischaracterization objection seems considerably more promising than its largely negative reception has suggested. We argue that the burden of proof is thus on philosophers who still hold that the method of cases crucially relies on intuitive judgments about cases. Finally, we discuss whether conceptual engineering provides an alternative to the method of cases in light of the challenge from experimental philosophy. We argue that this is not clearly the case, because conceptual engineering also requires descriptive information about the concepts it aims to improve. However, its primarily normative perspective on our concepts makes it largely orthogonal to the challenge from experimental philosophy, and it can also benefit from the empirical methods of the latter.