The prototypical solution-processable polymer of intrinsic microporosity, PIM-1, and derivatives thereof offer combinations of permeability and selectivity that make them potential candidate materials for membrane-based gas separations. Paramount to the design and evaluation of PIMs for economical natural gas sweetening is a high and stable CO 2 /CH 4 selectivity under realistic, mixed-gas conditions. Here, amidoxime-functionalized PIM-1 (AO-PIM-1) was prepared and examined for fundamental structure/property relationships. Qualitative NLDFT pore-size distribution analyses of physisorption isotherms (N 2 at -196 o C; CO 2 at 0 o C) reveal a tightened microstructure indicating size-sieving ultra-microporosity (<7Å). AO-PIM-1 demonstrated a three-fold increase in α D (CO 2 /CH 4 ) over PIM-1, surpassing the 2008 upper bound with P(CO 2 )=1153Barrer and ideal α(CO 2 /CH 4 )=34. Under a 50:50 CO 2 :CH 4 mixed-gas feed, AO-PIM-1 showed less selectivity loss than PIM-1, maintaining a mixed-gas α(CO 2 /CH 4 ) ~21 across a 20bar pressure range. Conversely, PIM-1 endured up to 60% increases in mixed-gas CH 4 permeability over pure-gas values concurrent with a selectivity of only ~8 at 20bar. A pervasive intermolecular hydrogen bonding network in AO-PIM-1 predominantly yields a rigidified microstructure that mitigates CO 2 -induced matrix dilations, reducing detrimental mixed-gas CH 4 copermeation.