A burner at which fuel cannot be combusted with air as the only source of oxygen for combustion in a stable flame at the burner when the feed rate of the fuel is too low, when the fuel is fed at too high an air-to-fuel mass ratio, when the fuel contains too high an amount of inert matter, or when the specific energy content of the fuel is too low, is modified by supplying oxidant containing more than 21 vol. % oxygen into the base of a flame at the burner, whereupon such fuels can be combusted at the burner.