The paper offers an account of the structure of information provided by models that relevantly deviate from reality. It is argued that accounts of scientific modeling according to which a model’s epistemic and pragmatic relevance stems from the alleged fact that models give access to possibilities fail. First, it seems that there are models that do not give access to possibilities, for what they describe is impossible. Secondly, it appears that having access to a possibility is epistemically and pragmatically idle. Based on these observations, an alternative is developed.