  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 $p(H)d \log H \propto
H^\gamma d \log H$. 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 $\gamma$. 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 $\gamma \approx 0$ or even $\gamma =0.5$. 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 $\gamma\
\sgreat\ 0$, then it would be interesting to look for MeV bursts in the future.
