Carbonaceous material, preferably coal or like finely divided solids with a mean particle diameter of 30 to 250 microns, is burned to produce steam in a fluid-bed furnace having a lower free space without internal fixtures and provided above this free space with internal cooling surfaces. A secondary-gas inlet introduces the secondary gas so that the volume ratio of fluidizing gas to secondary gas ranges from 1:20 to 2:1 at a location above the fluidizing-gas and fuel inlets but below the internal cooling surfaces, the gas velocity of the several gases being adjusted so that the mean suspension density of the solids above the secondary-gas inlet is 15 to 100 kg/m.sup.3. Approximately stoidiometric conditions are maintained with respect to the oxygen in the gases introduced and the carbonaceous material and solids are recycled to the bed after being separated from the gases emanating therefrom.