Is there cosmological time dilation in gamma-ray bursts?

Norris et al. report that the temporal structure of faint gamma-ray bursts is longer than that of bright bursts, as expected for time dilation in the cosmological models of burst origin. I show that the observed trends can easily be produced by a burst luminosity function and thus may not result from cosmological effects. A cosmological signature may be present, but the tests Norris et al. present are not powerful enough to detect these signatures.