Comprehensive studies of the luminescence of p–i–n structures with 10 compensated GaAs/AlGaAs quantum wells have been performed. The studies were carried out in the terahertz (THz) and near-infrared (NIR) spectral ranges with both optical and electrical pumping of nonequilibrium charge carriers. The THz photoluminescence spectra revealed an emission line caused by electron transitions from the first size-quantization subband e1 to the ground levels of donors D1s. The photo- and electroluminescence spectra in the NIR range revealed an emission line caused by electron transitions from the D1s levels to the first subband of heavy holes hh1. These transitions provide effective depletion of the D1s levels and are therefore relevant for creating a THz emitter operating at e1–D1s transitions. At high injection currents in the p–i–n diode, lasing occurs at the D1s–hh1 transitions, which increases the efficiency of depletion of the D1s levels. It is shown that for a given optical pump power or injection current density, the overall rate of the D1s–hh1 transitions in the p–i–n structure with 10 QWs is significantly higher than in similar structure with 50 QWs.