The observation by the BATSE experiment on board the Compton Gamma-Ray
Observatory (CGRO) that the gamma-ray burst population is isotropic b
ut inhomogeneous has dramatically bolstered the premise that most burs
ts are cosmological. At the same time, BATSE has also observed definit
e spectral breaks (Schaefer et al (1992) between 400 keV and 2 MeV in
some bursts, which in three cases have been corroborated by data from
EGRET. The presence of these breaks in these sources suggests attenuat
ion by the pair production mechanism gammagamma --> e+e-, which can ab
sorb gamma rays, though it is suppressed when the radiation is highly
beamed. In this paper, quantitative constraints that pair production p
laces on radiation collimation in individual sources, due to the prese
nce or absence of breaks in spectra, are presented. Cosmological burst
s have extremely relativistic beaming, though the bulk Lorentz factors
of their emission regions are reduced markedly for steep source spect
ra. Such beaming will blueshift the breaks to higher energies, indicat
ing that those CGRO bursts displaying MeV spectral breaks may not be c
osmological, or perhaps that their breaks are generated by mechanisms
that dominate gamma-gamma attenuation at MeV energies. Alternative mec
hanisms for break production are discussed.