Quantum-cascade-laser- (QCL) pumped molecular lasers (QPMLs) have recently been introduced as a source of powerful ($>\phantom{\rule{-2pt}{0ex}}1$ mW) tunable THz) narrow-band ($<\phantom{\rule{-2pt}{0ex}}10$ kHz) continuous-wave terahertz radiation. The performance these depends critically on collision physics, pump saturation, and the design laser cavity. Using validated three-level mod...