  We put forward a method to optimize the step-tapering amplitude of undulator
strength and initial energy detuning of electron beam with the goal of
maximizing the saturation power of high-gain FELs, based on the physics of
longitudinal electron beam phase space. Using the FEL simulation code GENESIS,
we numerically demonstrate the accuracy of the estimation for parameters
corresponding to the linac coherent light source and the Tesla test facility.
