A basic fact about Cohen reals is that adding λ Cohen reals cannot produce more than λ of Cohen reals. More precisely, if 〈rα|α < λ〉 are λ-Cohen generic reals over V , then in V [〈rα|α < λ〉] there is no λ -Cohen generic real over V . But if instead of dealing with one universe V we consider two, then the above may no longer be true. The purpose of this paper is to produce models V1 ⊆ V2 such th...