We have identified two types of bursts with luminosities that differ by about an order of magnitude. The more luminous HE bursts are identified by strong high-energy flux(E>300 keV).The dimmer NHE bursts are identified by a marked lack of high-energy flux. The spectral properties that are used to identify these two burst populations are also influenced by redshifting in the cosmological scenario. The observed burst spectral and intensity data are compared to both a cosmological model with a monoluminous burst population and a cosmological model containing two burst populations with distinctly different luminosities. These comparisons are used to characterize the luminosity difference between HE and NHE bursts more accurately as well as to evaluate the consistency between the redshifting effects and the shape of the intensity distribution for the two models. ©1998 American Institute of Physics.