Maximum luminosity of a SN below strong CSM interaction as a function of the resulting total luminosity and the ratio f_V. SNe that are classified as IIn are found in the region f_V< 0.15 (yellow-coloured area; limit best suited for IIP-CSM) and there is a corresponding upper limit in the maximum luminosity of the underlying transient. The luminosity range for most well-studied samples of SNe IIn is indicated by the cyan colour. LOSS, CCCP, and CSP stand for the samples of Li et al. (2011b), Kiewe et al. (2012) and Taddia et al. (2013), respectively. 1σ and 2σ contours for the luminosity functions of the core-collapse SNe adopted here are shown as vertical bars. A few horizontal and vertical dashed lines are drawn to guide the eye. It is shown that the faintest (M ≳ −17.2) SNe IIn cannot hide a SN IIP that is brighter than M = −15.