Polymers of intrinsic microporosity (PIMs), such as the archetypal spirobisindane-based PIM-1, are among the most promising new materials for making gas separation membranes with high permeance for potential use in high-throughput applications. Here it is shown that ultrapermeable PIMs can be prepared by fusing rigid and bulky triptycene (Trip) to the spirobisindane (SBI) unit. PIM-SBI-Trip and its copolymer with PIM-1 (PIM-1/SBI-Trip) are both ultrapermeable after methanol treatment (PCO2 > 20 000 Barrer). Old films, although less permeable, are more selective and therefore provide data that are close to the recently redefined Robeson upper bounds for the important CO2/CH4, CO2/N2, and O2/N2 gas pairs. Temperature-dependent permeation measurements and analysis of the entropic and energetic contributions of the gas transport parameters show that the enhanced performance of these polymers is governed by strong size-sieving character, mainly due to the energetic term of the diffusivity, and related to their high rigidity. Both polymers show a relatively weak pressure-dependence in mixed gas permeability experiments up to 6 bar, suggesting a potential use for CO2 capture from flue gas or for the upgrading of biogas.