A class of conceptual optimum refrigeration cycles is considered with a fixed overall heat conductance and a specified refrigerant operating temperature range to bound the optimization problems. These cycles deal with maximum refrigeration power, maximum refrigeration load, and maximum heat rejection load for the case of a heat pump. The resulting one degree of freedom problems are solved with a variable arithmetic mean temperature difference in the heat exchangers. The maximum refrigeration power solution yields an analytical closed form optimality rule which constitutes a close lower bound solution to the maximum refrigeration load and maximum heat rejection load problems. ©1995 American Institute of Physics.