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It is well known that Gamma-ray Burst spectra often display a break atenergies $\simless 400$ keV, with some exceptions extending to several MeV.\ \Modeling of a cosmological source population is thus non-trivial when comparingthe catalogs from instruments with different energy windows since this spectralstructure is redshifted across the trigger channels at varying levels ofsensitivity. We here include this important effect in an attempt to reconcileall 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 uniformlydistributed in a \qo $=1/2$ universe with no evolution can account very wellfor the combined set of observations. We show that the source population cannotbe truncated at a minimum redshift $z_{min}$ beyond $\sim 0.1$, and suggestthat a simple follow-on instrument to BATSE, with the same trigger window, nodirectionality and 18 times better sensitivity might be able to distinguishbetween 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.Comment: 12pages + 3 figures (available from ptamblyn@as.arizona.edu),  plainTeX, SO-93-112

Reconciliation of the Disparate Gamma-Ray Burst Catalogs in the Context of a Cosmological Source Distribution