  We theoretically revisit the problem of the propagation of coherent light
pulses through a linear medium when the carrier frequency of the pulses
coincides with the minimum of a narrow dip in the medium transmission.
Considering realistic contrasts between the maximum and minimum transmission of
the medium and incident pulses of strictly finite duration, we combine temporal
and spectral approaches to obtain analytical expressions of the transmitted
pulse that reproduce the main features of the exact numerical solutions derived
by fast Fourier transform. A special attention is paid to the advance of the
pulse maximum over that of a pulse covering the same distance in vacuum and the
ratio of this advance to the pulse duration (fractional advance) is optimized.
