The dynamics of self-induced transparency in an inhomogeneously broadened attenuator is investigated with special emphasis on delay times. One finds a strong dependence of delay times on the input value of the area parameter $\ensuremath{\theta}$ with pulses of ${\ensuremath{\theta}}_{\mathrm{in}}\ensuremath{\approx}\ensuremath{\pi}$ exhibiting much larger delay times than for ${\ensuremath{\theta}}_{\mathrm{in}}=2\ensuremath{\pi}$. This investigation is extended to include the effects of an atomic phase memory time ${T}_{2}$ which is of the order of ten times the pulse width (i.e., in accord with current experimental circumstances). The variation of other parameters is considered. A method of measuring $\ensuremath{\theta}$ directly is presented.