Case-control comparisons are a gold standard method for diagnosing and researching neuropsychological deficits and dissociations at the single-case level. These statistical tests, developed by John Crawford and collaborators, provide quantitative criteria for the classical concepts of deficit, dissociation and double-dissociation. Much attention has been given to the control of Type I (false positive) errors for these tests, but far less to the avoidance of Type II (false negative) errors; that is, to statistical power. I will describe the origins and limits of statistical power for case-control comparisons, showing that there are hard upper limits on power, which have important implications for the design and interpretation of single-case studies. My aim is to stimulate discussion of the inferential status of single-case neuropsychological evidence, particularly with respect to contemporary ideals of open science and study preregistration.