Two homopolyesters and a series of novel random copolyesters were synthesized from two bio-based diacid esters, dimethyl 2,5-furandicarboxylate, a well-known renewable monomer, and dimethyl 2,2'-bifuran-5,5'-dicarboxylate, a more uncommon diacid based on biochemical furfural. Compared to homopolyesters poly(butylene furanoate) (PBF) and poly(butylene bifuranoate) (PBBf), their random copolyesters differed dramatically in that their melting temperatures were either lowered significantly or they showed no crystallinity at all. However, the thermal stabilities of the homopolyesters and the copolyesters were comparable. Based on tensile tests from amorphous film specimens, it was concluded that the elastic moduli, tensile strengths, and elongation at break values for all copolyesters were similar as well, irrespective of the furan:bifuran molar ratio. Tensile moduli of approximately 2 GPa and tensile strengths up to 66 MPa were observed for amorphous film specimens prepared from the copolyesters. However, copolymerizing bifuran units into PBF allowed the glass transition temperature to be increased by increasing the amount of bifuran units. Besides enhancing the glass transition temperatures, the bifuran units also conferred the copolyesters with significant UV absorbance. This combined with the highly amorphous nature of the copolyesters allowed them to be melt-pressed into highly transparent films with very low ultraviolet light transmission. It was also found that furan-bifuran copolyesters could be as effective, or better, oxygen barrier materials as neat PBF or PBBf, which themselves were found superior to common barrier polyesters such as PET