We investigate the visibility of signals characterised by wide bumps over a
smoothly falling background that cannot be accurately predicted by Monte Carlo
calculations. Examples of such are the wide bumps that triboson and quadriboson
resonance cascade decays would yield in diboson resonance searches in fully
hadronic final states. We find that the sensitivity to triboson bumps is rather
small: signals of a moderate size could be present in current data and yet
remain unnoticed. For quadriboson cascade decays the signals can hardly be
distinguished from the background in the current searches.