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A simple and compact scheme that enhances the brightness of self‐amplified spontaneous‐emission (SASE) free‐electron lasers is presented. The method combines the high‐brightness SASE scheme and the optical klystron concept to increase the temporal coherence of the produced radiation and to reduce the required length of the undulator beamline at the same time. The scheme is very simple and only requires compact chicanes between the modules of the undulator beamline. Simulations show that, in comparison with SASE, the brightness can be improved by up to a factor of ten and the required length to achieve saturation can be reduced by 20% or more. [ABSTRACT FROM AUTHOR]