The relation evidentiality bears on the coding of some information as presupposition or as implicature is still an underexplored research field. In this paper, such an interplay is addressed by looking into how presupposed and implied contents (differently) respond to contexts of challenge and deniability. As taken for granted information (Stalnaker, Robert. 1973. Presuppositions. Journal of Philosophical Logic 2(4). 447–457), presupposition is more resistant to both challenging and retracting conversational moves, since it conveys content the speaker does not commit to. By contrast, implicature – characterized as intentional meaning (Grice, Herbert P. 1975. Logic and conversation. In Peter Cole & Jerry Morgan (eds.), Syntax and semantics 3: Speech acts, 41–58. New York: Academic Press) – allows both challenging and retracting conversational moves, because it is information the speaker commits to the most, similarly to what happens with plain declarative sentences. Building on this account, it is suggested that the higher challenging and deniability status cued by implicature is related to its function of encoding a direct type of evidentiality (Aikhenvald, Alexandra Y. 2004. Evidentiality. Oxford: Oxford University Press), namely a condition in which the speaker presents herself as the first-hand source of some information. Conversely, the weaker challengeability and deniability associated to presupposition hinges on its property of encoding a mutual type of evidentiality (Hintz, Daniel J. & Hintz Diane M. 2017. The evidential category of mutual knowledge in Quechua. Lingua 186. 88–109), that is, a state in which information is construed and conveyed as already shared by all participants at the moment of utterance.