A feasibility analysis on mechanically compressed vapor cycle systems is practiced in accordance with the laws of thermodynamics. The feasibility is mathematically expressed in three different factors: the expansion valve exit quality, the compressor effeciency, and the cooling efficiency. Numerical results are plotted in the figures to form illustrative feasibility diagrams; from which found are permissible combinations of the evaporation/condensation temperatures, the required compression ratio, and the required compressor efficiency. An evaporation temperature control method, coupled with the thermohydraulic analysis procedure, is then introduced for a space-borne heat pump system operating under off-design conditions. Control variables used in that method are the compression ratio and the compressor speed, requested values of which are graphically shown in the figures with parameters of interest. In addition to compressed vapor systems, this paper deals with pumped single/two-phase fluid ones. A computational approach based on analytical modeling is proposed for the heat rejection system trade-off study and has resulted in unified system/subsystem design procedures. Demonstrative examples of design calculations are explained with figures; displaying the liquid/vapor line diameters, the system weight breakdown, the specific weight, the specific power, and the compressor speed.