Knowledge and epistemic necessity

Claims of the form ??I know P and it might be that not-P?? tend to sound odd. One natural explanation of this oddity is that the conjuncts are semantically incompatible: in its core epistemic use, ??Might P?? is true in a speaker??s mouth only if the speaker does not know that not-P. In this paper I defend this view against an alternative proposal that has been advocated by Trent Dougherty and Patrick Rysiew and elaborated upon in Jeremy Fantl and Matthew McGrath??s recent Knowledge in an Uncertain World.