Edge emitting, terahertz quantum cascade photonic-wire lasers, based on a third order Bragg grating are presented. Devices with a power consumption as low as 300mW, with a single frequency output power of more than 1.5mW are demonstrated. Their maximum operating temperature in continuous-wave mode operation is 110K and the emission is concentrated in a narrow beam (~30 degrees divergence). Larger structure based on the same design show more than 10mW output power and more than 200mW/A slope efficiency at 10K continuous-wave operation.