Abstract: A refrigeration appliance is provided having at least two refrigeration compartments, each compartment having its own access door. The appliance includes a single evaporator located in a plenum which is selectively in communication with each of the compartments, a single compressor, preferably run by a variable speed motor, and a refrigerant circuit including a series of conduits for providing a flow of refrigerant to the evaporator and compressor. A control determines which of the compartments is demanding cooling and operates the refrigeration device until the detected demand for cooling has been satisfied for the particular compartment. Prior to terminating the operation of the refrigeration device, the control determines if the second compartment is demanding cooling or was within a predetermined temperature range prior to demanding cooling. If either condition exists, the refrigeration device is switched to the second compartment until the demand for cooling therein has been satisfied.