Left panel: distribution of the improvement of the CPL fit with respect to the PL fit, for 1000 fake spectra. All fake spectra have been simulated adopting the best fit model obtained fitting a PL model to the observed spectrum of GRB 080928. A δℒ > 11 corresponds to a probability <1% to have a stochastic improvement (horizontal red line in the figure). The δℒ obtained when the real spectrum is fitted with a PL and a CPL is δℒ_PL−CPL = 59, corresponding to a chance probability much smaller than 1%. Right panel: as in the left panel, but the PL fits are compared to BPL fits. Also in this case, the improvement δℒ = 162 exceeds the critical value of 12.