Melt transesterification polycondensation enabled the incorporation of rigid, cycloaliphatic diols (2,2,4,4-tetramethylcyclobutane-1,3-diol) into decahydronaphthalene-containing copolyesters, which resulted in amorphous, optically clear materials. Glass transition temperatures approached 155°C and followed predictable trends using the Fox equation for randomly sequenced copolymers. Dynamic mechanical analysis identified several low-temperature relaxations attributed to the complex motions of the decahydronaphthalate and cyclohexyl rings within the polymer backbone. Furthermore, incorporating cyclobutane rings suppressed the low-temperature local mobility, revealing a strong structural dependence on these relaxations. The rheological simplicity of these nonassociating chains permitted analysis over a large frequency window using time–temperature superposition. As a result, the characteristic relaxation times provided insight into chain dynamics and the propensity for chain entanglements. Finally, positron annihilation lifetime spectroscopy probed hole-free volume and reinforced the trends observed with oxygen permeability measurements.