This paper deals with the conditions under which singular definites, on the one hand, and universally quantified DPs, on the other hand, receive interpretations according to which the sets denoted by the NP-complements of the respective determiner vary with the situations quantified over by a Q-adverb. I show that in both cases such interpretations depend on the availability of situation predicates that are compatible with the presuppositions associated with the respective determiner, as co-variation in both cases comes about via the binding of a covert situation variable that is contained within the NP-complement of the respective determiner. Secondly, I offer an account for the observation that the availability of a co-varying interpretation is more constrained in the case of universally quantified DPs than in the case of singular definites, as far as word order is concerned. This is shown to follow from the fact that co-varying definites in contrast to universally quantified DPs are inherently focus-marked.