Indefinites have been a traditional hunting ground for approaches like Discourse Representation Theory, Situation Semantics and Dynamic Semantics for some 40 years now. Choosing amongst these approaches, that appear to be intensionally so different, has turned out to be quite elusive, to the point that one wonders whether they are, in fact, all distinguishable. Maybe, ‘Natural Logic’, i.e. the set of logical capacities that manifests itself through language, hopelessly underdetermines the issue. In the present paper, I bring into this debate a set of very familiar data that, however, has never been considered relevant to the debate on indefinites, namely crossover phenomena, and argue that they may provide key evidence for a dynamic take, once a non-standard mapping hypothesis is adopted. Usually, in DS one assumes that Discourse Referents are activated by Noun Phrases (i.e. arguments); I propose instead that DRs can only be activated by predicates (Dynamic Predication). This conceptually simple assumption is shown to have far reaching consequences, among others that of yielding a new take on Weak Crossover.