A scheme for generating coherent radiation at latest generation low emittance storage rings such as PETRA III at DESY is proposed. The scheme is based on focusing and subsequent defocusing of the electron beam in the longitudinal phase space at the undulator location. The expected performance characteristics are estimated for radiation in the wavelength range of 500–1500 eV. It is shown that the average brightness is increased by several orders of magnitude compared to spontaneous undulator radiation, which can open new perspectives for photon-hungry soft X-ray spectroscopy techniques.