In this talk I draw a distinction between the direct and indirect contribution of a mental state to the epistemic justification of a belief. In terms of this distinction, I describe a puzzle surrounding the conditions on which S's direct justification for believing P originating from S's seeming that P is defeated. According to a traditional answer stemming from Pollock, the direct justification from the seeming can be undercut by evidence D that its seeming to one that P does not reliably indicate that P is true. However, the distinction between the direct and indirect contribution motivates the expectation that this should not be so, and that D should just be able to undercut S's indirect justification from the seeming. This leaves unexplained why, when S acquires D, S is apparently left with no justification for believing P. I begin by pre-empting a possible dissolution of this puzzle inspired by Glüer's doxastic account of perceptual experience. Then I explore three solutions to this puzzle. The third one, which I defend, conjectures that D affects S's direct justification from the seeming not by undercutting it but by rebutting one presupposition of it