  In the use and interpretation of $\log{N}$--$\log{S}$ distributions for
gamma-ray bursts, burst peak flux has typically been used for $S$. We consider
here the use of the fluence as a measure of $S$, which may be a more
appropriate quantity than the peak flux in such highly variable sources. We
demonstrate how using the BATSE trigger data we can determine the selection
effects on fluence. Then using techniques developed elsewhere to account for
the important threshold effects and correlations. Applying the appropriate
corrections to the distributions, we obtain a fluence distribution which shows
a somewhat sharper break than the peak flux distribution, implying a possibly
narrower fluence luminosity distribution. If bursts are at cosmological
distances, these observations together indicate that evolution of the
luminosity function is required.
