Stojnic ́ et al. (Philos Perspect 27(1):502–525, 2013; Linguist Philos 40(5):519–547, 2017) argue that the reference of demonstratives is fixed without any contribution from the extra-linguistic context. On their ‘prominence/coherence’ theory, the reference of a demonstrative expression depends only on its context-independent linguistic meaning. Here, we argue that Stojnic ́ et al.’s striking claims can be maintained in only the thinnest technical sense. Instead of eliminating appeals to the extra-linguistic context, we show how the prominence/coherence theory merely suppresses them. Then we ask why one might be tempted to try and offer such a view. Since we are rather sympathetic to the motivations we find, we close by sketching a more plausible alternative.