A motor vehicle headlight has a light source, a reflector co-operating with the light source to form a beam of predetermined photometry, a housing which contains the reflector and the lamp that includes the light source, and a cover glass closing the front of the housing. An adjusting device is provided for varying the orientation of the beam by pivoting the reflector about a tilting axis. The lamp is mounted in a fixed position in the casing, and the tilting axis of the reflector passes close to the light source. The adjusting device includes a rotary maneuvering member having a driving spigot which is eccentric to the axis of rotation of the maneuvering member. The spigot is arranged to slide, substantially without clearance, in a slot formed in an element fixed to the reflector. This slot is oriented substantially transversely to the axis of the rotary member and transversely to the direction of displacement of the reflector. The rotary member can be turned freely on itself over more than 360.degree..The invention is applicable in particular to complementary headlights such as long range driving lights or fog lights.