The invention relates to a high-pressure gas discharge lamp, particularly a motorcar lamp, comprising a bulb including at least two neck portions and a vacuum-tight discharge vessel of quartz glass, at least two electrodes projecting into the discharge vessel, and a filling in the discharge vessel which, in the operating state, is in a discharge state. Such lamps are used, in particular, in headlights of motorcars. In order to ensure that the arc of the high-pressure gas discharge lamp generates a higher luminescence in a small area, and the lamp can be used as a light source in motorcar headlights, the discharge vessel of the high-pressure gas discharge lamp in accordance with the invention encloses a discharge space having a width B below 4 mm and a length C below 8 mm, and the filling comprises NaI, ScI3, Xe, ZnI3 and is free of Hg. Surprisingly it has been found that the use ZnI2 in the filling causes the arc to generate a higher luminescence in the area of the arc axis per dimension of the arc. In the case of motorcar headlights, forming the desired light beam on the street requires the light source to be as punctiform as possible, i.e. the highest possible luminescence is generated in a small area. This enables the design of the reflector to be improved and the arc to be more accurately projected on the street. This applies also to headlights comprising an optical projection system instead of a reflector.