This paper presents a structural account of the shift from directly referential to non-directly referential interpretation of nominal expressions with strong definite articles in Austro-Bavarian German and demonstratives in English. I propose that such DPs involve a functional projection headed by a relational predicate which can host either a silent individual pronoun, which gives rise to the directly referential behaviour, or a restrictive relative clause, which gives rise to covarying interpretations. The paper thus translates into structural terms the recent proposals that DPs with demonstratives/strong articles have a greater semantic complexity than "regular" Fregean definites (Nunberg 1993, Elbourne 2008a, Schwarz 2009, Elbourne 2013). Previous approaches to this problem did not take into account the role of relative clauses, which are present in the overwhelming majority of non-directly referential uses of English complex demonstratives (King 2001, Dever 2001, Powell 2001).