Standard GRB, Dirty Fireballs, and the Excluded Middle

Abstract: 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 $5.3 \times 10<sup>{-3}$ erg/$\rm cm² y$, 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.