We investigate, independently of specific emission models, the constraints on
the value of the bulk Lorentz factor Gamma of a fireball. We assume that the
burst emission comes from internal shocks in a region transparent to Thomson
scattering and before deceleration due to the swept up external matter is
effective. We consider the role of Compton drag in decelerating fast moving
shells before they interact with slower ones, thus limiting the possible
differences in bulk Lorentz factor of shells. Tighter constraints on the
possible range of Gamma are derived by requiring that the internal shocks
transform more than a few per cent of the bulk energy into radiation. Efficient
bursts may require a hierarchical scenario, where a shell undergoes multiple
interactions with other shells. We conclude that fireballs with average Lorentz
factors larger than 1000 are unlikely to give rise to the observed bursts.Comment: 5 pages, 3 figures, accepted for publication in MNRAS, pink page
