In earlier work, it was found that sulfur oxide emissions could be markedly reduced by injecting finely divided limestone into a coal-burning, fluidized bed operating at 1500F to 1600F and with about 3% residual oxygen in the flue gas. However, with 3% residual oxygen in the flue gas, an economically unacceptable fraction of the input coal's fuel value would be lost as carbon in the flyash that is blown out of the furnace. A comprehensive search for methods to reduce the loss of fuel, which ranged as high as 15%, led to the invention of the Carbon-Burnup Cell. The Carbon-Burnup Cell is a region of a fluidized bed boiler in which the fuel is the carbon bearing flyash carried out of the adjacent coal burning regions of the boiler. The report describes an effort to produce design criteria for an effective Carbon-Burnup Cell. The experimental work was conducted in two different test rigs. The more basic work, that which led to a statistically derived performance model, was done in a separate column which depends on an external source for its fuel supply. The second set of tests was performed in an actual fluidized-bed boiler, generating the flyash which is then immediately burned in its own internal flyash fired section, the prototype Carbon-Burnup Cell. The work in the boiler led to engineering insights on the design requirements for a commercial fluidized-bed boiler which included a Carbon-Burnup Cell. A performance model and costs are included.