  We revisit the optimization of performance of finite-time Carnot machines
satisfying the low-dissipation assumption. The standard procedure seeks to
optimize an objective function, such as power output of the engine, over the
durations of contacts between the working medium and the heat reservoirs. This
procedure may lead to unwieldy equations at the optimum of some objective
functions. We propose an alternate scheme in which the output or input work is
first optimized for a given cycle time, followed by an optimization of another
objective function over the cycle time. The optimal behavior is thus obtained
in a much simplified manner, with closed-form expressions for figures of merit.
The approach is demonstrated for various objective functions, both for engines
as well as refrigerators.
