Use of two heat rejection temperatures instead of one for a heat-driven heat pump is shown to reduce spacecraft waste heat radiator area and heat rejection system mass. The optimum high rejection temperature T1 is shown to be somewhat less than Kerrebrock's rule, three-fourths of the heat source temperature TH. The optimum low rejection temperature T2 is 50-80 K above the cooling load temperature Tc. General results are presented based upon the assumption of constant fractions of Carnot efficiency for the heat engine and refrigerator, and specific results are reported for a mercury-vapor engine coupled to an isobutane-R113 binary refrigerator. A single dimensionless grouping composed of ratios of equipment mass per unit power to radiator mass per unit area, and the ratios of the sink temperature Ts and cooling load temperature Tc to TH, are shown to be the major parameters characterizing the advantages of a spacecraft heat pump. Nomenclature A = radiator area, m2 a = radiator mass per unit area, kg/m2 B - equipment to radiator parameter, b/a, m2/W b - equipment mass per unit power, kg/W C = constants in nonlinear models, Eqs. (19) and (20) c - constant in mass relationship, Eq. (6), kg h = specific enthalpy, J/kg M =mass, kg p - pressure, N/m2 Q = heat flow, W s = specific entropy, J/kg K T = temperature, K W = mechanical power or heat flow of high availability, W e = radiator emissivity f = Carnot efficiency or COP ry = component isentropic efficiency a = Stefan-Boltzmann constant = fraction of Carnot efficiency or COP