Based on a model of a two-heat-reservoir heat-engine cycle with a finite high-temperature source and bypass heat-leak, in which the maximum work output can be obtained under a given cycle time is determined with the considerations of heat-leak, finite heat-capacity high-temperature source and infinite heat-capacity low-temperature heat-sink with another linear heat-transfer law Q proportional to Delta(T-1). The heat-engine cycles considered are: (1) infinite low-and high-temperature reservoirs without heat-leak; (2) infinite low- and high-temperature reservoirs with heat-leak, (3) finite high-temperature source and infinite low-temperature sink without heat-leak and (4) finite high-temperature source and infinite low-temperature sink with heat-leak. It is assumed that the heat-transfer between the working fluid and the reservoirs obeys another linear heat-transfer law, i.e., the linear phenomenological heat-transfer law, Q proportional to Delta(T-1). It is shown that the existence of heat-leak does not affect the configuration of a cycle with an infinite high-temperature source. The finite heat-capacity of the high-temperature source without heat-leak makes the cycle a generalized Carnot heat-engine cycle. There exists a great difference of the cycle configurations for the finite high-temperature source with heat-leak and the former three cases. Moreover, the relations between the optimal poweroutput and the efficiency of the former three configurations are derived, and they show that the heat-leak affects the power versus efficiency characteristics of the heat-engine cycles. (c) 2004 Elsevier Ltd. All rights reserved.