Oxygen-scavenging polyester compositions are disclosed that include residues of one or more unsaturated diols having from 4 to 8 carbon atoms, in an amount from about 0.01 mole percent to about 10 mole percent, and residues of terephthalic acid in an amount of at least 50 mole percent, in each case based on the total amount of residues of dicarboxylic acids in the polyester composition comprising 100 mole percent. The polyester compositions typically have an intrinsic viscosity that is at least 0.65 dL/g.