The preparation and characterization of new, tailor-made polymeric membranes using poly(styrene-b-butadiene-b-styrene) (SBS) triblock copolymers for gas separation are reported. Structural differences in the copolymer membranes, obtained by manipulation of the self-assembly of the block copolymers in solution, are characterized using atomic force microscopy, transmission electron microscopy, and the transport properties of three gases (CO2, N2, and CH4). The CH4/N2 ideal selectivity of 7.2, the highest value ever reported for block copolymers, with CH4 permeability of 41 Barrer, is obtained with a membrane containing the higher amount of polybutadiene (79 wt%) and characterized by a hexagonal array of columnar polystyrene cylinders normal to the membrane surface. Membranes with such a high separation factor are able to ease the exploitation of natural gas with high N2 content. The CO2/N2 ideal selectivity of 50, coupled with a CO2 permeability of 289 Barrer, makes SBS a good candidate for the preparation of membranes for the post-combustion capture of carbon dioxide.