Based on Basque data (and in line with Etxeberria & Giannakidou 2010, to appear), this paper argues that the domain for quantifiers in certain languages is restricted overtly by a definite determiner (D). This strategy of domain restriction via D--DDR--happens by applying DDR to the nominal argument, but DDR can also apply to the Q-det itself, in which case it forms a constituent with it. In both cases, DDR is a type preserving function, i.e. a modifier, and supplies the contextual C variable. This analysis provides support for the program that domain restriction is syntactically realized, but an important refinement is proposed: domain restriction can affect the Q-det itself (pace Stanley 2002), and in fact quite systematically in certain languages. The Qdet that is affected by DDR is typically a strong one. So-called weak quantifiers cannot be contextually restricted by DDR. Crucially in Basque, D only appears with strong quantifiers.