The optimal coefficient of performance (COP) of a class of two-heat-reservoir refrigeration cycles can be determined by a given cycle time and absorbed heat (cooling load) with consideration of heat leak, finite heat capacity low-temperature source and infinite heat capacity high-temperature heat sink. The refrigeration cycles considered in this paper include (1) infinite low-and high-temperature reservoirs without heat leak, (2) infinite low-and high-temperature reservoirs with heat leak, (3) finite low-temperature source and infinite high-temperature sink without heat leak, and (4) finite low-temperature source and infinite high-temperature sink with heat leak. It is assumed that the heat transfer between the working fluid and the reservoirs obeys Newton＇s law. It is shown that the existence of the heat leak does not affect the optimal configuration of a cycle with an infinite low-temperature source. The finite heat capacity of a low temperature source without heat leak makes the cycle a generalized Carnot refrigeration cycle. There exists a great difference of the cycle configurations for the finite low temperature source with heat leak and the former three cases. Moreover, the relations between the optimal cooling load and the COP of the former three configurations are derived, and they show that the heat leak affects the cooling load versus COP characteristics of the refrigeration cycles.