When bounded by two infinite thermal reservoirs, the theory of irreversible thermodynamics for reciprocating externally irreversible cycles yields to an optimum efficiency at maximum power output of η = 1−(TL/TH)0.5 for internally reversible Stirling-like cycles using regeneration and linear heat transfer modes is in contrast to the upper limit for Stirling cycles of η = 1−(TL/TH) obtained from classical thermodynamics. This optimum behavior is, however, only based on cycle temperature bounds. For reciprocating cycles one must go a step further and minimize cycle time. While executing this new step for finite thermal reservoirs, it was discovered that, for the general family of reciprocating Stirling-like cycles, the finite-time optimum work output (Wopt) at maximum power is less than (and in the limit of ideal regeneration, infinite reservoirs and of no internal irreversibility, is equal to) exactly one-half of the work of the externally reversible cycle operating at maximum thermal efficiency (Carnot work, Wrev) between the same temperature limits (i.e., Wopt ⩽ ½Wrev). To accomplish this the analysis goes beyond earlier works to use time symmetry to better optimize overall cycle power. Because this procedure results in the concurrent employment of the first and second laws of thermodynamics, it ensures optimal allocation of thermal conductances at the hot and cold ends while simultaneously achieving both minimization of internal entropy generation and maximization of specific cycle work for a given set of operating temperatures. Based on linear heat transfer laws, this expression for optimum work is shown to be independent of heat conductances. Finally, the analysis establishes that the maximum power attainable for a Stirling-like reciprocating cycle operating between two temperature bounds is always less than (and in the limit of power optimized Carnot conditions, equal to) one-half of that obtained for the continuous counterpart of the same cycle operating between the same temperature bounds. © 1998 American Institute of Physics.