Typical SASE XFEL pulses exhibit poor longitudinal coherence, a characteristic inherited from the start-up from shot noise. Self-seeding schemes are an answer to the call for improved longitudinal coherence. If applied to already working or designed XFELs, these schemes are subject to constraints, including minimal change to the baseline design, and possibility to recover the baseline mode of operation. In this work we propose a novel single-bunch self-seeding method, based on a particular kind of monochromator that satisfies these constraints. We will limit ourselves to the analysis of the simplest possible configuration, consisting of an input undulator and an output undulator, separated by our novel monochromatization stage. Such a stage consists of a weak few-meter long chicane, acting as a tunable delay stage, washing out the electron beam microbunching, and creating a transverse offset for the monochromator. In essence, the monochromator consists of a single crystal in Bragg-transmission geometry, which operates as a bandstop filter for the transmitted X-ray SASE radiation pulse. When the incident angle and the spectral contents of the incoming beam satisfy the Bragg diffraction condition, the temporal waveform of the transmitted radiation pulse shows a long monochromatic tail, whose duration is inversely proportional to the bandwidth of the absorption line in the transmittance spectrum. The magnetic chicane is tuned to shift the electron bunch on top of the monochromatic wake created by the bandstop filter thus selecting (temporal windowing) a part of the wake. By this, the electron bunch is seeded with a radiation pulse characterized by a bandwidth much narrower than the natural FEL bandwidth. The output power from our setup can be further increased by tapering the magnetic field of the undulator, yielding a tremendous increase in peak brightness with respect to the baseline mode of operation. In this work we present a feasibility study and exemplifications for the LCLS, and we discuss advantages of our method compared to other self-seeding techniques.