This manuscript describes the gas separation performance of PIM-2, a partially fluorinated linear copolymer synthesized from 5,5′,6,6′-tetrahydroxy-3,3,3′,3′-tetramethylspirobisindane (TTSBI) and decafluorobiphenyl (DFBP). As one of the early members of the family of polymers of intrinsic microporosity, it had never been tested as a gas separation membrane because of insufficient mechanical resistance. This has been solved only recently, allowing the preparation of robust self-standing films. Molecular modelling studies demonstrated a high fractional free volume (34%) and an elevated surface area (642 m2 g−1), and the latter is in good agreement with experimental BET results. Pure gas permeabilities measured on a fixed-volume time-lag instrument at 1 bar compare well with the results of mixed separation tests on a variable volume setup from 1-6 bar(a). Molecular modelling and independent sorption measurements on a gravimetric sorption balance both show strong dual-mode sorption behaviour, especially for CO2 and to a lesser extent for CH4. Temperature-dependent pure gas permeation measurements show typical Arrhenius behaviour, with a clear increase in the activation energy for diffusion with the increasing molecular size of the gas, indicating high size-selectivity. This is in agreement with the highly rigid PIM structure, determined by AFM force spectroscopy measurements. The dual-mode behaviour results in a moderate pressure dependence of the CO2 permeability and the CO2/N2 and CO2/CH4 selectivity, all slightly decreasing with increasing pressure. The presence of humidity in the gas stream has a remarkable small effect on the membrane performance, which is probably due to the high fluorine content and the consequently low water vapour solubility in the polymer, as confirmed by gravimetric sorption measurements. The manuscript describes an extensive study on the structure-property relationships in PIM-2.