A high-pressure gas discharge lamp (HID or UHP lamp, or in general lamps with mercury fillings of between approximately 0.05 and 0.5 mg/mm.sup.3) is described with at least one electrode (7, 8) which is provided with a thickened, for example globular portion (9, 10) at its end lying inside a lamp vessel (2). This portion is so dimensioned in dependence on operational parameters of the lamp and/or the diameter of the electrode rod that an electrode tip (19) forms itself independently at said portion during the first hours of operation. This tip grows from the portion until its free end starts melting. The electrode tip is self-adjusting in this manner, so that an optimum electrode interspacing is maintained throughout lamp life. Furthermore, a method of manufacturing such a lamp is described.