This paper describes the transformation of lambda-terms from continuation-passing style (CPS) to direct style. This transformation is the left inverse of Plotkin's left-to-right call-by-value CPS encoding for the pure lambda-calculus. Not all -terms are CPS terms, and not all CPS terms encode a left-to-right call-by-value evaluation. These CPS terms are characterized here; they can be mapped back to direct style. In addition, the two transformations -- to continuation-passing style and to direct style -- are factored using a language where all intermediate values are named and their computation is sequentialized. The issue of proper tail-recursion is also addressed.