a method for providing cooling air to the venturi and the combustion chamber in a low nox emission combustor as used in a gas turbine engine that includes the steps of providing an annular air passage surrounding said combustion chamber and venturi where said cooling air under pressure enters the combustion chamber / venturi near the aft portion of the combustion chamber , passing the air along the combustion chamber , past the venturi where the air exits near the front portion of the convergent area of the venturi . the method prevents any channel / passage cooling air from being received into the combustion chamber , and at the same time , introduces the outlet of the cooling air , after the air has passed over the combustion chamber of the venturi and has been heated , back into the premix chamber thereby improving the efficiency of the combustor while reducing and lowering nox emission in the combustion process . in an alternate embodiment , a combustion system is disclosed incorporating a shaped deflector to direct cooling air into a cooling passageway of a venturi . the deflector is configured to provide a cooling system with increased total pressure to increase overall cooling effectiveness .