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A report is presented on GaAs/(Al,Ga)As terahertz (THz) quantum-cascade lasers (QCLs) based on alternating photon and longitudinal optical (LO) phonon-assisted transitions between quasi-minibands. The design is optimised for low threshold current densities and low operating voltages, resulting in reduced ohmic heating during continuous-wave (CW) operation. The QCLs exhibit lasing over a broad range of frequencies from 2.91 to 3.21 THz. Using single-plasmon waveguides, pulsed operation up to 114 K and CW operation up to 65 K has been achieved.