Using a perturbative approach, we perform a quantitative three-dimensional analysis of slow-light enhanced traveling wave amplification in an active semiconductor photonic crystal waveguide. The impact of slow-light propagation on the carrier-depletion-induced nonlinear gain saturation of the device is investigated. An effective rate-equation-based model is presented. It is shown that it well accounts for the three-dimensional simulation results. Simulations indicate that a slow-light-enhanced photonic crystal traveling-wave amplifier has a high small-signal modal gain and low saturation power.