A new homopolymer, 6FDA-CARDO(t-Bu), was prepared from 6FDA-CARDO through one-step chemical modification by adding bulky tert-butyl groups, using Friedel–Crafts alkylation. The incorporation of the bulky groups led to a significant increase in the fractional free volume (FFV) within the matrix of membranes prepared from the modified polymer. The thermal properties of the modified polymer were not greatly affected compared to those of its parent 6FDA-CARDO homopolymer, where the Td5% and the Tg were measured to be 517 °C and 366 °C, respectively. The hydrazine-assisted cleavage of 6FDA-CARDO(t-Bu) led to the preparation of the new diamine monomer CARDO(t-Bu) in high yield. Pure-gas and multicomponent sweet and sour mixed-gas permeation studies of dense films prepared from 6FDA-CARDO(t-Bu) were carried out and compared to those of membranes prepared from 6FDA-CARDO. For example, the carbon dioxide (CO2) pure-gas permeability of the 6FDA-CARDO(t-Bu) membrane was measured at 100 psi feed pressure and 22 °C, and found to be 271 Barrer which is 4.6-fold higher when compared to that of 6FDA-CARDO membranes. Due to a simultaneous increase in the methane (CH4) pure-gas permeability, a reduction in the CO2/CH4 selectivity of the 6FDA-CARDO(t-Bu) membrane was recorded. A similar effect was observed for the sweet mixed-gas separation studies. Interestingly, the sour mixed-gas (containing 21% hydrogen sulfide, H2S) separation properties of the 6FDA-CARDO(t-Bu) membrane showed a different trend. At 500 psi and 22 °C, the H2S/CH4 selectivity was 10% higher, and the CO2 and H2S permeability coefficients were 3.2- and 3.8-fold, respectively, higher compared to those obtained for 6FDA-CARDO membranes.