We demonstrate an effective mode selector design that enables a terahertz quantum cascade wire laser to have a robust single-mode operation at frequencies much lower than the gain peak. This is achieved by selectively guiding the undesired modes into a lossy session while keeping the desired lasing mode largely unperturbed. The large mode discrimination obtained by this mode selector is necessary to further extend the tuning range to the lower half of the gain curve. Additionally, the connectors of this mode selector conveniently provide electrical bias to the wire lasers without degrading the lasing performance.