A high-pressure discharge lamp for motor vehicle headlamps having a mercury-free ionizable fill which consists of xenon with a cold filling pressure of at least 2000 hPa and metal halides. The discharge vessel has a tubular section (10) which consists of a transparent ceramic and has an internal diameter which is less than or equal to 2 mm and inside which there are arranged electrodes with a spacing less than or equal to 10 mm.