Standard GRB, Dirty Fireballs, and the Excluded Middle
  It is shown that the contribution of faint gamma-ray bursts (GRB) to the total allsky GRB energy flux is small. The allsky flux of GRB appears to be $5.3 \times 10^{-3}$ erg/$\rm cm^2 y$, with little additional component hidden within weak or otherwise undetectable GRB. This significantly constrains physical models of GRB and dirty fireballs, suggesting a rather sharp dichotomy between them should the latter exist. 
David Eichler
astro-ph.HE