Here, we report the synthesis of two polysulfones containing either triptycene or phenolphthalein as the bulky bridging unit in the polymer backbone to investigate the influence of the rigid, unwieldy structures on chain rigidity, fractional free volume, and gas transport properties. Incorporation of the triptycene unit provided the most rigid backbone, greatest fractional free volume, and strongest gas separation performance, because of its exceptional combinations of permeability and selectivity, relative to many commercial polymers and other polysulfones reported in the literature. In addition, integration of the triptycene unit and its intrinsic, configuration-based free volume provided good resistance to physical aging. In particular, the triptycene-based polysulfone experienced exceptional H-2/CH4 selectivity (156) combined with nearly doubled H-2 permeability, as well as promising O-2/N-2 separation performance with an O-2 permeability of 1.5 Barrer, which is an similar to 21% increase, relative to that of the bisphenol A-based commercial polysulfone, to go along with an O-2/N-2 selectivity of 7.7.