In the scope theory of intensionality, world variables are incorporated into content word denotations and valued by a parameter of interpretation in such a way that an expression's evaluation world is determined by its structural position. In the binding theory of intensionality, by contrast, world variables are instantiated by pronouns that saturate arguments introduced by content words and that need not be locally bound. One challenge for the scope theory comes from Bäuerle (1983), who points out cases where the scope theory seemingly leads to contradictory assumptions about a sentence's LF. Keshet (2010) attempts to reconcile Bäuerle's challenge with the scope theory by treating indefinites as choice functions rather than as quantifiers. In this paper, I argue that Keshet's solution depends on assumptions regarding the behavior of choice functions in intensional contexts that create difficulty in accounting for de re readings of indefinites embedded under two or more attitude predicates. The conclusion is that, even if we admit choice function technology, Bäuerle's challenge remains a problem for the scope theory of intensionality.