Terahertz (THz) quantum cascade lasers (QCLs) have undergone rapid development since their demonstration, showing high power, broad-tunability, quantum-limited linewidth, and ultra-broadband gain. Typically, to address applications needs, continuous-wave (CW) operation, low-divergent beam profiles and fine spectral control of the emitted radiation, are required. This, however, is very difficult to achieve in practice. Lithographic patterning has been extensively used to this purpose (via distributed feedback (DFB), photonic crystals or microcavities), to optimize either the beam divergence or the emission frequency, or, both of them simultaneously, in third-order DFBs, via a demanding fabrication procedure that precisely constrains the mode index to 3. Here, we demonstrate wire DFB THz QCLs, in which feedback is provided by a sinusoidal corrugation of the cavity, defining the frequency, while light extraction is ensured by an array of surface holes. This new architecture, extendable to a broad range of far-infrared frequencies, has led to the achievement of low-divergent beams (10°), single-mode emission, high slope efficiencies (250 mW/A), and stable CW operation.