 Within the space of cancellation-based accounts of presupposition, it is hard to beat Gazdar’s for its conceptual and technical simplicity, and its empirical coverage. Some conceptual questions remain, however, such as why it should be that presuppositions are the last things to be added in the process of updating commitments. Van der Sandt’s (1982, 1988) reformulation of the cancellation model gives us an alternative way to think about this, by modeling projection in terms of whether presuppositions could have come first.