A method is provided for achieving low NOx in the operation of a non-premixed combustion system by reacting a fuel-rich mixture to produce partial reaction products plus heat, transferring a portion of the heat to a bypass air stream, and passing the cooled partial reaction products into non-premixed contact and combustion with a stoichiometric portion of the heated bypass air stream. A supply of fuel and a supply of air is provided; and a fuel-rich mixture is formed and reacted to produce partial reaction products plus a heat of reaction. A portion of the heat of reaction is transferred to a bypass air stream and the cooled partial reaction products are passed into non-premixed contact and combustion with a stoichiometric portion of the heated bypass air stream.