A high-pressure discharge lamp which is suitable for motor vehicle headlights, has an improved color point stability close to the black body locus, a high color temperature, and a high luminous efficacy (lm/w). The high-pressure discharge lamp includes an inner vessel with a discharge chamber, with at least two electrodes extending into the discharge chamber, and an outer bulb surrounding the inner vessel. The discharge chamber contains an ionizable filling including at least one rare gas, 0-10 mg of mercury, and a metal halide mixture. The metal halide mixture includes 40-80% by weight of sodium halide, 25-55% by weight of scandium halide, 1-15% by weight of indium halide, and 0-34% by weight of thallium halide.