Good explanations are not only true or probably true, but are also relevant to a causal question. Current models of causal explanation either only address the question of the truth of an explanation, or do not distinguish the probability of an explanation from its relevance. The tasks of scenario construction and conversational explanation are distinguished, which in turn shows how scenarios can interact with conversational principles to determine the truth and relevance of explanations. The proposed model distinguishes causal discounting from causal backgrounding , and makes predictions concerning the differential effects of contextual information about alternative explanations on: (a) the kind of mental models constructed; (b) belief revision about probable cause; and (c) the perceived quality of a focal explanation. Four experiments are reported that test these predictions. The significance of the notion of explanatory relevance for research on causal explanation is then discussed.