**Abstract** This paper extends the analysis of modal subordination presented in Stone (1999); Stone and Hardt (1999) to other cases of non-veridically introduced discourse referents (drefs) with the goal of understanding the circumstances under which a dref is available for subsequent anaphoric reference. The central claim is that a dref introduced under negation can be the antecedent for a pronoun, only if the interpretation does not require that the assertion of its non-existence and the existence presupposition of the pronoun be true wrt the same set of worlds. The analysis is based on relativizing individual drefs to the worlds in which their referent exists (Stone (1999); Stone and Hardt (1999)), and sentential operators introducing propositional drefs that provide a local context for the interpretation of their prejacent (Karttunen (1973); Heim (1983)), and it is framed in intensional CDRT (Muskens (1996); Brasoveanu (2007, 2010)). This allows for a greater empirical coverage than Krahmer and Muskens's (1995) account of drefs under negation and disjunction.