A lighting device for a motor vehicle includes a housing having a front lighting surface, and a substantially planar plate and at least one lighting module mounted on the plate. The plate has a general plane of extension that is horizontal when the housing is mounted in the vehicle, and has a surface referred to as a lower surface and a surface referred to as an upper surface. The plate includes a first control system which includes a first male element and is arranged to cause translation of the first male element in an axis parallel to the plate, the plate being provided with a first recess receiving the first male element. A second control system that includes a second male element and is arranged to cause translation of the second male element in an axis perpendicular to the plate, the plate being provided with a second recess on its upper or lower surface that receives the second male element. The housing thus takes up less space above the modules, which can easily be raised.