Natural gas purification is a challenging task due to the existing number of contaminants in the mixture. Sour natural gas, in particular, presents an even higher challenge due to the presence of the highly toxic hydrogen sulfide (H2S) gas. These contaminants level must be reduced to meet the sales gas specifications. In this paper, three DAM-based random copolymers were prepared for simultaneous improvement of the acid gases (CO2 and H2S) separation properties of their corresponding membranes. While the developed membranes exhibit high CO2/CH4 selectivity in a non-sour mixed-gas, their unconventional behavior during sour gas separation is difficult to predict. Therefore, their membranes were subjected to sour mixed-gas separation tests a quinary gas mixture including 20 vol% H2S at different upstream pressures up to 34.5 bar. Each membrane demonstrated one or more improved properties in terms of acid gases permeability and selectivity coefficients. Taking into consideration the overall performance, membranes prepared from 6FDA-DAM/6FpDA (1:3) exhibited the most attractive separation properties among the series prepared. However, based on the relatively high H2S/CH4 selectivity obtained of 6FDA-DAM/CARDO (1:3) membranes, a block 6FDA-DAM/6FDA-CARDO (1:1) copolyimide was prepared, and the sour mixed-gas separation properties were evaluated. The overall block copolymer membrane demonstrated very attractive productivity and efficiency, compared to the standard industrially used glassy polymer, cellulose acetate, thereby rendering it a potential candidate for sour natural gas purification.