  We show that the brighter gamma-ray bursts (GRBs) in the BATSE 3B catalog
concentrate slightly toward the Galactic plane and center, suggesting that at
least some bursts originate within the Galaxy. To develop an interpretation of
this brightness-dependent anisotropy, we consider GRBs distributed in a thick
disk centered on the Galaxy. As an approximation to the true luminosity
distribution, we divide bursts into two distinct luminosity classes. Most
bursts originate from low-luminosity, nearby sources while the relatively few
high-luminosity sources trace the shape of the thick disk. We find that
characteristic disk dimensions as small as 20 kpc in thickness and 30 kpc in
radial extent can match the observed brightness-dependent anisotropy as well as
the number-flux distribution; these dimensions are smaller than previously
considered viable. For bursts distributed in a disk of these compact
dimensions, the low-luminosity sources must have peak powers of $\lapprox
5\times 10^{40}$ erg s$^{-1}$ and rate densities of $\gapprox 5\times 10^{-3}$
yr$^{-1}$ kpc$^{-3}$. The high-luminosity sources must have a peak luminosity
of $\simeq 10^{42}$ erg s$^{-1}$ but their rate density need be only 5% or less
than that of the low-luminosity sources. If the Andromeda Galaxy contained a
similar population of high-luminosity sources, their peak gamma-ray fluxes
would be less than $\sim 0.1$ s$^{-1}$ cm$^{-2}$, making their detection
problematic. Statistical analyses of the gamma-ray burst events obtained since
the compilation of the 3B catalog will determine whether the thick-disk
interpretation is preferred over the isotropic one.
