Sentences involving disjunctions under a possibility modal give rise to so-called ‘free choice’ inferences, i.e. inferences to the effect that each disjunct is possible. This note investigates the interaction between free choice and presupposition projection. We focus on sentences embedding both a disjunction in the scope of a possibility modal and a presupposition trigger, and we investigate how the free choice inference triggered by the former can contribute to filtering the presupposition of the latter. We consider three cases: conditionals, disjunctions and unless sentences. We observe that in all of these cases the presuppositions triggered from the consequent, second disjunct, or the scope of unless appear to be filtered by a free choice inference associated with the rest of the sentence. The case of the conditional can be accommodated by scalar accounts of free choice, but the disjunction and unless cases cause a substantial problem for all these accounts. After discarding a natural but unsuccessful attempt at a solution, we consider two more promising strategies. The first holds on to an implicature account of free choice and exploits an algorithm of free insertion of redundant material. The second exploits a semantic account of free choice. Each of these solutions comes with related problems. We conclude that the correct form of a theory of free choice remains open, though the data concerning the interaction between free choice and presupposition can significantly help sharpen our theoretical choices.