Blazars exhibit flares with a doubling time-scale of the order of minutes. Such rapid flares are theoretically challenging and several models have been put forward to explain the fast variability. In this paper, we continue the discussion concerning the effects of non-linear, time-dependent synchrotron self-Compton (SSC) cooling. In previous papers, we were able to show that the non-linearity, introduced by a time-dependent electron injection, has severe consequences for both the spectral energy distribution (SED) and the monochromatic synchrotron light curve. The non-linear cooling introduces novel breaks in the SED, which are usually explained by complicated underlying electron distributions, while the much faster cooling of the SSC process causes significant differences in the synchrotron light curves. In this paper, we calculate the inverse Compton light curves, taking into account both the SSC and the external Compton process. The light curves are calculated from the monochromatic intensities by introducing the retardation due to the finite size of the emission region and the geometry of the source. Even though some of the obvious effects of the SSC cooling are washed out by the retardation, there are still several observational constraints which could help to discriminate between the non-linear and the usual linear models, such as different flux states, temporal shapes or faster variability of the light curves at different energies.