  The inhomogeneous brightness distribution of BATSE detected gamma-ray bursts
has been considered strong evidence for their cosmological origin. However,
subclasses of gamma-ray bursts have been shown to have significantly more
homogeneous brightness distributions. Pendleton et al. (1997) have found such a
result for gamma-ray bursts with no detectable emission at energies >300 keV.
Accordingly, it has been suggested that these no high energy (NHE) emission
bursts represent an underluminous population of nearby sources. A distinct
homogeneous NHE brightness distribution has also been considered as evidence
for beaming of different spectral components of the prompt burst emission. We
synthesize observed distributions of gamma-ray bursts based on a sample of
typical bright BATSE bursts with intrinsic high energy emission and adopt a
single cosmological distance scale for all sources. We find that the resulting
synthetic NHE bursts do indeed have a more nearly homogeneous intensity
distribution when an appropriate decrease in signal to noise and redshifted
spectrum is incorporated. We argue that the definition of NHE bursts, and
soft-spectrum bursts in general, naturally produces a steep distribution. The
NHE class of gamma-ray bursts is therefore likely due to brightness bias.
