We demonstrate experimentally a terahertz frequency quantum-cascade laser which can be tuned electronically, in a step-wise manner from typically 3.07 to 3.40 THz, by changing the applied electric field across the device. To achieve this, the gallium growth rate was successively reduced during growth of the active region from +6% to −4% of its nominal 1 μm/h operating value. This produced a heterogeneous active region, comprising 23 sections of different lasing units stacked together. With a single-metal surface-plasmon waveguide configuration, the devices operated in pulsed mode, up to a temperature of 81 K, and gave peak powers of ∼8 mW.