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.