Among the polymer families, aliphatic polyesters stand out from this category thanks to their degradable and biocompatible properties. In particular, the gamma-lactones differ from other lactones by yielding polyesters that can be depolymerized back to the monomer and offer the advantage of counting various biobased monomers. As an example, alpha-hydroxy- gamma-butyrolactone (HBL) is a hydroxy-functionalized monomer that can be obtained by a biological synthetic route from glucose. In this article, the ring-opening copolymerization (ROCP) of HBL and L-lactide (LLA) using t-BuP4 as catalyst is investigated. The copolymerizations were conducted within a temperature range of 5-100 degrees C, affording monomer conversions exceeding 80%. The characterization of the copolyesters revealed a branched structure consisting of different HBL patterns, including cyclic, linear, and branched motives. Performing a kinetic study of the copolymerization at room temperature provided a deeper understanding of the mechanism. By modulating the reaction parameters, copolymers of low molar masses with an HBL content of up to 33% were synthesized. High molar mass LLA/HBL-based copolyesters, with Mw up to 290,000 g/mol, were synthesized by a straightforward chain coupling reaction with a diisocyanate.