We adapt the "reverse taper" scheme presented by Saldin et al. (Phys. Rev. ST Accel. Beams, 9, 050702 [2006]) for attosecond pulse production to the XUV/soft-xray regime. We find that that GW-level pulses of a few femtosecond duration or shorter can be produced using electron beams of quite moderate parameters and undulators of 20-m length or shorter. The output pulse is significantly shifted in wavelength relative to the main background which permits a further increase in contrast ratio via simple monochromatization. Moreover, the output pulse has a natural wavelength chirp that allows further temporal compression, if wanted. Both positive and negative chirps can be produced depending upon the sign of the undulator taper.