  We have analyzed the transmission properties of pulses through
one-dimensional periodic structures in order to systematically explore the best
conditions to achieve the maximum delay with the minimum possible distortion.
In the absence of absorption and no layer variation, the transmission
coefficient $t_N$ can be well approximated by a sum of Lorentzian resonances.
The ratio between their width $\Gamma_{\rm r}$ and their separation
$\Delta\omega_{\rm r}$ is a crucial parameter to characterize the distortion of
the transmitted pulse. For typical values of the parameters used in
telecommunications and high index of refraction contrasts $n_2 / n_1$, the
distortion of the transmitted pulse is unacceptably large for frequencies near
the edge of the transmission window. We estimate fractional delays achievables
in terms of the central frequency used and the pulse bandwidth.
