  While it is generally agreed that the emitting regions in Gamma-Ray Bursts
(GRBs) move ultra relativistically towards the observer, different estimates of
the initial Lorentz factors, $\Gamma_0$, lead to different, at times
conflicting estimates. We show here that the quiet periods in which the signals
goes down below the instrumental thresholds, put strong upper limits on the
values of $\Gamma_0$. According to the standard internal-external shocks model
an external shock should develop during the prompt stage. This external shock
radiates in the hard X-rays to soft gamma-rays bands and this emission should
be seen as a smooth background signal. The observed deep minima indicate that
this contribution is negligible. This limits, in turn, $\Gamma_0$. We obtain
upper limits on $\Gamma_0$ for several bursts with typical values around
hundreds. We compare these values with those obtained by the other methods,
which typically yield lower limits. The results are marginally consistent
leaving only a narrow range of allowed values for $\Gamma_0$.
