Nonlinear harmonics in X-ray FELs can be parasitically produced as soon as FEL reaches saturation, or can be radiated in dedicated afterburners. In both cases there is a strong background at the fundamental, since it is much stronger than harmonics. One can get around this problem by application of the recently proposed reverse undulator tapering. In this contribution we present numerical simulations of harmonic production in such a configuration as well as recent results from FLASH where the second and the third harmonics were efficiently generated with a low background at the fundamental. We also present the results for a high-contrast operation when the afterburner is tuned to the fundamental
