  The early X-ray afterglow for a significant number of gamma-ray bursts
detected by the Swift satellite is observed to have a phase of very slow flux
decline with time ($F_\nu \propto t^{-\alpha}$ with $0.2 \lesssim \alpha
\lesssim 0.8$) for $10^{2.5} s \lesssim t \lesssim 10^4$ s, while the
subsequent decline is the usual $1 \lesssim \alpha_3 \lesssim 1.5$ behavior,
that was seen in the pre-Swift era. We show that this behavior is a natural
consequence of a small spread in the Lorentz factor of the ejecta, by a factor
of $\sim 2-4$, where the slower ejecta gradually catch-up with the shocked
external medium, thus increasing the energy of forward shock and delaying its
deceleration. The end of the ``shallow'' flux decay stage marks the beginning
of the Blandford-McKee self similar external shock evolution. This suggests
that most of the energy in the relativistic outflow is in material with a
Lorentz factor of $\sim 30-50$.
