After taking into account threshold effects, we find that the isotropic‐equivalent energiesEisoand luminositiesLisoof gamma‐ray bursts (GRBs) are correlated with redshift at the 5&percent; and 0.9&percent; signficance levels, respectively. Our results are based on 10BeppoSAX GRBs and 11 HETE‐2 GRBs with known redshifts. Our results suggest that the isotropic‐equivalent energies and luminosities of GRBs increase with redshift. They strengthen earlier clues to this effect from analyses of the BATSE catalog of GRBs, using the variability of burst time histories as an estimator of burst luminosities (and therefore redshifts), and from an analysis ofBeppoSAX bursts only. If the isotropic‐equivalent energies and luminosities of GRBs really do increase with redshift, it suggests that GRB jets at high redshifts may be narrower and thus the cores of GRB progenitor stars at high redshifts may be rotating more rapidly. It also suggests that GRBs at very high redshifts may be more luminous — and therefore easier to detect — than has been thought, which would make GRBs a more powerful probe of cosmology and the early universe than has been thought. © 2004 American Institute of Physics