  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.
