Entropically driven ring-opening copolymerization of mixtures of a fraction of cyclic oligo(hexamethylene terephthalate)s composed of cycle sizes from 2 to 5 and p-dioxanone was used to prepare random copolyesters covering a range of aromatic (HT) to aliphatic (DO) units ratios from 9 to 1.3. The composition and microstructure of the copolyesters were accurately determined by H-1 and C-13 NMR, respectively. The copolyesters showed thermal degradation and glass transition temperatures in good agreement with their comonomeric composition and microstructure, and they crystallized for contents in DO less than 30%, adopting the same crystal structure as poly(hexamethylene terephthalate). The copolyesters appeared to be sensitive to hydrolytic degradation, which was observed to take place superficially with the generation of non-water-soluble degraded fragments and with the release of water-soluble dioxanoic acid to the aqueous medium.