A method for providing uniform heat distribution within a furnace as well as decreasing the amount of NOx in the combustion products, when operating an industrial furnace having at least one conventional burner using air as the oxidant. At least one lance is connected with the furnace, and an oxidant including oxygen gas is flowed into the furnace through the lance to impinge against a flame issuing from the burner at a certain impingement point. The amount of oxygen supplied by the air supply to the burner together with the amount of oxidant issuing from the lance corresponds with the stoichiometric amount for a fuel supplied to the burner. At least 50% of the supplied oxygen for combustion is supplied through the lancing of oxidant, and the oxidant is flowed into the furnace through the lance at a velocity of at least 200 m/s.