Copolymerization of xylitol usually yields cross-linked materials. In this work, microwave-assisted polyesterification of xylitol and succinic acid produced materials with diverse molecular weights and different branching degrees, and more importantly, no cross-linking was observed, as supported by the solubility behavior and spectroscopic data. Reactions were carried out for short times, less than 20 min, which is not common for production of industrial polyesters. Control over the branching degree was achieved by tuning the reaction conditions, such as temperature, time of exposure, and monomer ratio, during microwave irradiation. No solvent or catalyst was employed during the step-growth polymerization.