Joint planning consists of people making proposals for future actions and events, and others accepting or rejecting these proposals. While proposals convey their speakers’ judgments of some ideas as feasible, however, in anticipation of and in an attempt to pre-empt the recipients’ rejection of their proposals, the speakers may begin to express doubt with the feasibility of their proposals. It is such ‘‘post-proposal displays of uncertainty,’’ and their interactional corollaries, that this paper focuses on. Drawing on video-recorded planning meetings as data, and conversation analysis as a method, I describe three ways for the recipients to respond to post-proposal displays of uncertainty: the recipients may (1) overcome, (2) confirm, or (3) dispel their co-participants’ doubts. Even if the outcome of the proposal, in each case, is its abandonment, the analysis points out to important differences in how these response options treat the first speakers’ ‘‘proximal deontic claims’’ -- that is, their implicit assertions of rights to control the participants’ local interactional agenda. The paper concludes by discussing the idea of proximal deontics with reference to other related notions.