This paper combines an empirical argument about the lexical semantics of might with a preliminary description and theoretical account of a novel variety of implicatures. Empirically, I introduce the DISMISSIVE AGREEMENT paradigm, which shows that might semantically encodes nothing stronger than nonzero probability. Theoretically, I derive the fact that might often seems to suggest something stronger from the pragmatic norm that cooperative speakers will make claims that are strong enough to be relevant to the Question Under Discussion, which gives rise to LOWER BOUND IMPLICATURES.