A composition of and a method of making high performance hollow fiber membranes is described. The membranes have a high resistance to plasticization by use of a predetermined amount of crosslinking. The preferred polymer material for the membrane is a polyimide polymer comprising covalently bonded ester crosslinks. The resultant hollow fiber membrane exhibits a high permeability of CO2 in combination with a high CO2/CH4 selectivity. Another embodiment provides a method of making the hollow fiber membrane from a monesterified polymer followed by final crosslinking after hollow fiber formation.