Many sentences can be interpreted both as a metaphor and as a literal claim, depending on the context. The aim of this paper is to show that there are discourse-based systematic constraints on the identification of an utterance as metaphorical, literal, or both (as in the case of twice-apt metaphors), from a normative point of view. We claim that the key is contextual coherence. In order to substantiate this claim, we introduce a novel notion of context as a rich and (...) heterogeneous body of information, including previous discourse, elements coming from the surroundings of the utterance, background information, and Questions Under Discussion (QUD) issued from these three sources. We then define contextual coherence as a relation between what we call the minimal paraphrase of the metaphor and the context, and argue that for an interpretation to be coherent two conditions must be met. First, the minimal paraphrase must address some question in the QUD stack. Second, it must be externally consistent, i.e. consistent with the available contextual information. Finally, we argue that an approach based on contextual coherence is better suited to deal with twice-true and twice-apt metaphors than traditional approaches based on semantic deviance or pragmatic lack of fit. (shrink)