It is often stated that gamma-ray bursts (GRBs) have typical energies of several hundred keV. Is this a real feature of GRBs or is it due to an observational bias? We consider the possibility that bursts of a given bolometric luminosity occur with a hardness distribution $p(H)d \log H \propto H^γd \log H$. We model the detection efficiency of BATSE as a function of $H$ and calculate the expected distribution of $H$ in the observed sample for various values of $γ$. We show that because the detection efficiency of BATSE falls steeply with increasing $H$, the paucity of hard bursts need not be real. We find that the observed sample is consistent with a distribution above $H = 100$ keV with $γ\approx 0$ or even $γ=0.5$. Thus, a large population of unobserved hard gamma-ray bursts may exist. It is important to extend the present analysis to a larger sample of BATSE bursts and to include the OSSE and COMPTEL limits. If the full sample is consistent with $γ \sgreat\ 0$, then it would be interesting to look for MeV bursts in the future.

5 pages, Latex using aps macros including one figure. Also available at ftp://shemesh.fiz.huji.ac.il or at http://shemesh.fiz.huji.ac.il/mev.ps To appear in Gamma-Ray Bursts, third workshop, Huntsville Oct-1995