Bounded rationality theories are typically characterized over exhaustive data sets. We develop a methodology to understand the empirical content of such theories with limited data, adapting the classic, revealed-preference approach to new forms of revealed information. We apply our approach to an array of theories, illustrating its versatility. We identify theories and datasets testable in the same elegant way as Rationality, and theories and datasets where testing is more challenging. We show that previous attempts to test consistency of limited data with bounded rationality theories are subject to a conceptual pitfall that may lead to false conclusions that the data is consistent with the theory.