The invention relates to a high-pressure discharge lamp for motor vehicle headlights which is provided with an annular flange (127) for mounting the high-pressure discharge lamp in the lamp holder of the motor vehicle headlight. According to the invention, the annular flange (127) is fixed on the base (125) by means of a snap or latching connection and is adapted to the lamp holder of motor vehicle headlights for halogen incandescent lamps. As a result, the high-pressure discharge lamp according to the invention can be inserted in motor vehicle headlights for halogen incandescent lamps.