The melt polymerization of diglycerol with bicyclic anhydride monomers derived from a naturally occurring monoterpene provides an avenue for polyesters with a high degree of sustainability. The hydrophobic anhydrides are synthesized at ambient temperature via a solvent-free Diels-Alder reaction of α-phellandrene with maleic anhydride. Subsequent melt polymerizations with tetra-functional diglycerol are effective under a range of [diglycerol]/[anhydride] ratios. The hydrophobicity of α-phellandrene directly impacts the swelling behavior of the resulting polyesters. The low E factors (<2), large amount of bio-based content (>75%), ambient temperature monomer synthesis, and polymer degradability represent key factors in the design of these sustainable polyesters.