An extended reality headset is configured to position and stabilize the headset on a face when worn. For example, the headset can include an external frame with first and second side pieces coupled to a display structure and configured to provide lateral stabilization. In some examples, the headset can include a front head-engaging structure front head-engaging structure that is rotationally coupled to the external frame via a pivot point. The headset can also include a rear head-engaging structure coupled the external frame. In some examples, the rear head-engaging structure can include a tensioning mechanism to adjust the headset to fit various head shapes. Additionally, the headset can include a flexible strap coupled to the front head-engaging structure and the tensioning mechanism. In some examples, applying tension to the flexible strap by the tensioning mechanism can cause the front head-engaging structure to rotate along the pivot point, providing a secure fit.