This paper deals with an unexpected contrast between demonstrative descriptions and definite descriptions on their anaphoric uses. If two (or more) discourse referents are introduced in the preceding sentence, it is perfectly natural to refer to one of them in the following sentence using a definite description. Use of demonstrative descriptions in the same context, however, is degraded, with existing accounts of anaphoric demonstratives and definites providing no explanation for this contrast. We present experimental evidence from two languages, one with definite determiners (English) and one without (Turkish), and show that the acceptability of demonstratives depends independently both on (i) whether one or two NPs are introduced in the initial sentence, and (ii) whether the follow-up sentence introduces a new situation or not. We propose a focus-driven information structural approach to demonstratives to account for this pattern. Following Dayal & Jiang (2021) (building on Schwarz 2009) in assuming that definite and demonstrative expressions in anaphoric contexts are similar in including an anaphoric index argument, we argue that demonstratives essentially differ in evoking focus alternatives on the index argument.