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.