I have two aims for the present paper, one narrow and one broad. The narrow aim is to show that a class of data originally described by Lynsey Wolter empirically undermine the leading treatments of complex demonstratives that have been described in the literature. The broader aim of the paper is to show that Wolter demonstratives, as I will call the constructions I focus on, are a threat not just to existing treatments, but to any possible theory that retains (...) the uncontroversial assumptions that relative clauses always form a constituent with the nouns they modify, and that semantic composition proceeds sequentially and locally, with the inputs to interpretation having the structure syntax tells us they do. (shrink)