A range of polyimides with characteristics similar to a polymer of intrinsic microporosity (PIM) were prepared by reaction with various aromatic diamines of a bis(carboxylic anhydride) incorporating a spiro-center. The polymers exhibited high surface area, as determined by nitrogen adsorption, and high thermal stability. Membrane gas permeation experiments showed PIM-polyimides to be among the most permeable of all polyimides and to have selectivities close to the upper bound for several important gas pairs. A group contribution method was used to predict permeability coefficients and separation factors for further PIM-polyimide structures, revealing worthwhile targets for future synthetic efforts.