A technique is described herein for determining a pose of at least one mobile controller. The technique involves using a transmitter to initially emit a magnetic field and/or electromagnetic radiation at an elevated-power level, with respect to a normal-use power level. A receiver detects the magnetic field and/or electromagnetic radiation, to provide received signals. A tracking component determines the pose of the controller based on the received signals. Thereafter, the technique transmits the magnetic field and/or electromagnetic radiation at the normal-use power level. In one implementation, a head-mounted display (HMD) uses the above-summarized technique to find the controller when the user initially dons the HMD. This is useful because the controller may be invisible to the user who dons the HMD because it is out-of-range with respect to the normal-use operating space of the HMD.