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The past decade has seen a protracted debate over the semantics of epistemic modals. According to contextualists, epistemic modals quantify over the possibilities compatible with some contextually determined group’s information. Relativists often object that contextualism fails to do justice to the way we assess utterances containing epistemic modals for truth or falsity. However, recent empirical work seems to cast doubt on the relativist’s claim, suggesting that ordinary speakers’ judgments about epistemic modals are more closely in line with contextualism than relativism (Knobe & Yalcin 2014; Khoo 2015). This paper furthers the debate by reporting new empirical research revealing a previously overlooked dimension of speakers’ truth-value judgments concerning epistemic modals. Our results show that these judgments vary systematically with the question under discussion in the conversational context in which the utterance is being assessed. We argue that this ‘QUD effect’ is difficult to explain if contextualism is true, but is readily explained by a suitably flexible form of relativism.