  It is well known that Gamma-ray Burst spectra often display a break at
energies $\simless 400$ keV, with some exceptions extending to several MeV.\ \
Modeling of a cosmological source population is thus non-trivial when comparing
the catalogs from instruments with different energy windows since this spectral
structure is redshifted across the trigger channels at varying levels of
sensitivity. We here include this important effect in an attempt to reconcile
all the available data sets and show that a model in which bursts have a
``standard'' spectral break at $300$ keV and occur in a population uniformly
distributed in a \qo $=1/2$ universe with no evolution can account very well
for the combined set of observations. We show that the source population cannot
be truncated at a minimum redshift $z_{min}$ beyond $\sim 0.1$, and suggest
that a simple follow-on instrument to BATSE, with the same trigger window, no
directionality and 18 times better sensitivity might be able to distinguish
between a \qo$=0.1$ and a \qo$=0.5$ universe in $3$ years of full sky coverage,
provided the source population has no luminosity evolution.
