Higher molecular weight polyesters are prepared from diacid anhydrides and cyclic alkylene carbonates by the process of first drying the reaction mixture either totally or at least substantially completely by azeotropic distillation of water using a suitable organic medium. The catalyst is then added and the polycondensation conducted as conventional. The polymers obtained are markedly higher in molecular weight than if the drying step is omitted, and the polycondensation period is dramatically shortened.