A high efficiency, Vortex Inertial Staged Air (VIStA) combustor provides ultra-low NO.sub.X production of about 20 ppmvd or less with CO emissions of less than 50 ppmvd, both at 3% O.sub.2. Prompt NO.sub.X production is reduced by partially reforming the fuel in a first combustion stage to CO and H.sub.2. This is achieved in the first stage by operating with a fuel rich mixture, and by recirculating partially oxidized combustion products, with control over stoichiometry, recirculation rate and residence time. Thermal NO.sub.X production is reduced in the first stage by reducing the occurrence of high temperature combustion gas regions. This is achieved by providing the first stage burner with a thoroughly pre-mixed fuel/oxidant composition, and by recirculating part of the combustion products to further mix the gases and provide a more uniform temperature in the first stage. In a second stage combustor thermal NO.sub.X production is controlled by inducing a large flow of flue gas recirculation in the second stage combustion zone to minimize the ultimate temperature of the flame. One or both of the first and second stage burners can be cooled to further reduce the combustion temperature and to improve the recirculation efficiency. Both of these factors tend to reduce production of NO.sub.X.