Multiblock copolymers based on both a PIM-PI block and a 6FDA-PI block, that are [(PIM-PI)x-b-(PI)y], with different block compositions (x:y= 1:4, 1:6 and 1:8) have been prepared for the first time. Through a combination of experimental and simulation approaches, the effects of the compositions of the PIM-PI units on the void distribution and gas transport properties in [(PIM-PI)x-b-(PI)y] block copolymer membranes are fully explored. By combining the effects of the high free volume of amorphous PIMs (polymers with intrinsic microporosity) brought about by the rigidity of the macromolecular chains and their contorted backbones with the excellent chemophysical properties of PIs (polyimides) in a block copolymer approach, our [(PIM-PI)x-b-(PI)y] membranes showed excellent thermomechanical properties as well as very good gas-separation performances, placing them well above the upper bound for CO2/N-2 and CO2/CH4, especially at low pressures, and making them comparable to even the highly permeable PIM-1. The block copolymer membrane, with a 1:4 block ratio between the (PIM-PI) and (6FDA-PI) units, denoted here as (PIM-PI)-b-(PI)(1:4), showed a well-connected morphology of the permeable phase and displayed very high CO2 permeability of 3011 Barrer as well as moderate CO2/CH4 (16.0) and CO2/N-2 (17.0) permselectivities, together with T-max above 520 degrees C and Young's modulus above 2.1 GPa.