High pressure vapor discharge lamp provided with a discharge vessel. The discharge vessel encloses a discharge space provided with a filling of mercury and a rare gas, for example, in a gastight manner. An electrode is arranged in the discharge space for generating and maintaining a discharge therein, while the electrode comprises a rod electrode having an enlarged head at its end which projects into the discharge space. According to the invention, the enlarged head comprises a preformed electrode projection having an at least substantially conical shape.