An advanced strategy for the optimal design and realization of a GaAs/AlGaAs quantum-cascade laser is presented. It relies on recently established inverse scattering techniques to design an optimal smooth active region profile, followed by a conversion to an almost equivalent digitally graded structure, comprising just two different alloy compositions. In order to compare the output characteristics of optimized and previously realized structures, the intersubband electron scattering transport in quantum cascade lasers is analyzed. A full self-consistent rate equation model which includes all relevant electron-longitudinal optical phonon and electron-electron scattering mechanisms between injector/collector, active region, and continuumlike states is employed. Whilst the gain coefficients and threshold currents calculated at 77 and 300 K for the structure with a standard triple quantum well active region show excellent agreement with recent experiments, a significant improvement of these parameters is predicted for the optimized digitally graded quantum-cascade laser.