As emphasized by Larry Laudan in developing the notion of non-refuting anomalies, traditional analyses of empirical adequacy have not paid enough attention to the fact that the latter does not only depend on a theory’s empirical consequences being true but also on them corresponding to the most salient phenomena in its domain of application. The purpose of this paper is to elucidate the notion of non-refuting anomaly. To this end, I critically examine Laudan’s account and provide a criterion to determine (...) when a non-refuting anomaly can be ascribed to the applicative domain of a theory. Unless this latter issue is clarified, no proper sense can be made of non-refuting anomalies, and no argument could be opposed to those cases where an arbitrary restriction in a theory’s domain of application dramatically reduces the possibilities for its empirical scrutiny. In arguing for the importance of this notion, I show how several semanticist resources can help to reveal its crucial implications, not only for theory evaluation, but also for understanding the nature of a theory’s applicative domain. (shrink)