We present three gamma-ray-burst spectra for bright bursts over very w
ide energy ranges. These were created from BATSE, COMPTEL, and OSSE da
ta. The three spectra are for GRB 910503 (from 20 keV to 300 MeV), GRB
910601 (from 28 keV to 10.5 MeV), and GRB 910814 (from 103 keV to 500
MeV). A composite spectrum of 19 bright bursts is presented from 41 k
eV to 1.9 MeV (with no weak lines visible) for use in calculating aver
age redshift corrections in cosmological models. Expanding fireball mo
dels with shocked synchrotron emission are predicted to have low-energ
y spectral slope (vF(v) proportional to v(alpha)) that asymptotically
approaches alpha = 4/3 such that alpha should never exceed 4/3. This p
rediction is tested with more than 100 bright bursts with BATSE and Gi
nga data. Over 90% of the bursts have spectral slopes in agreement wit
h this prediction. For only one burst (GRB 870303, which has reported
cyclotron lines) can a strong case be made that the slope violates the
model limit, and then only from 2-5 keV.