  We show that first several overtones could calculated by the time-domain
integration method for asymptotically de Sitter black holes already at the
lowest multipole numbers of gravitational and electromagnetic perturbations.
This is not possible for asymptotically flat black holes, for which extraction
of frequencies with the Prony method is usually possible with reasonable
accuracy only for the fundamental mode. The reason for much better efficiency
in the de Sitter case is absence of power-law tails: the quasinormal modes
dominate the signal not only at the intermediate stage, but also at
asymptotically late times.
