We show that the decomposition of Intuitionistic Logic into Linear Logic along the equation A \rightarrow B = !A \multimap B may be adapted into a decomposition of classical logic into LLP, the polarized version of Linear Logic. Firstly we build a categorical model of classical logic (a Control Category) from a categorical model of Linear Logic by a construction similar to the co-Kleisli category. Secondly we analyse two standard Continuation-Passing Style (CPS) translations, the Plotkin and the Krivine?s translations, which are shown to correspond to two embeddings of LLP into LL.