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. For example, Maria can go study in Tokyo or Boston suggests that Maria can go study in Tokyo and that she can go study in Boston (Kamp 1973). This note focuses on the interaction between free choice and presupposition projection. In particular, 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 (Fox 2007, Klinedinst 2007, Franke 2011 among others). We consider a solution based on free insertion of redundant material, building on an account of presupposition projection and anaphora recently proposed by Rothschild (2017). We point out that this account, combined with a scalar theory of free choice, provides a solution for our basic cases, but still has non-trivial problems with related more complex cases. We also point out that our data can instead be captured by some of the recent semantic accounts of free choice (Willer 2017, Aloni 2016 and Starr 2016), in combination with a standard algorithm for presupposition projection. We end by briefly discussing how these semantic accounts also have unsolved problems having to do with the interaction between certain downward entailing operators and free choice. We conclude that the correct form of a theory of free choice remains open to debate.