A new way to combine two different polymerisation reactions, using a single catalyst, results in efficient block polymer synthesis. The selective polymerisation of mixtures of l-lactide-O-carboxyanhydride and cyclohexene oxide, using a di-zinc catalyst in a one-pot procedure, allows the preparation of poly(l-lactide-b-cyclohexene carbonate). The catalysis near quantitatively recycles the carbon dioxide released during polyester formation into the subsequent polycarbonate block, with an atom economy of up to of 91%.