Analysis of the superdefomed rotational bands

All available experimental data for the $\Delta I=2$ transition energies in superdeformed bands are analyzed by using a new one-point formula. The existence of deviations from the smooth behavior is confirmed in many bands. However, we stress that one cannot necessarily speak about staggering patterns as they are mostly irregular. Simulations of the experimental data suggest that the irregularities may stem from the presence of irregular kinks in the rotational spectra. This could be a clue but, at the moment, where such kinks come from is an open question.