This paper proposes a new explanation of the well-known that-t effect, based on the assumption that the head-head relation is a matter of PF rather than of syntax. After critical review of some Minimalist approaches (Roussou 2002, Roberts and Roussou 2001, Pesetsky and Torrego 2001, 2002), a PF-based solution is proposed in terms of a generalization on the lexical realization of heads. In particular, this paper argues that the first head that is compatible with agreement must lexically host the Agr-feature of T on a phase basis. This solution turns out to be applicable to various data regarding the that-t effects across languages.