A high pressure discharge lamp may include a ceramic discharge vessel and a longitudinal axis, wherein at least one electrode is led out of the discharge vessel by means of a metal-containing feed-through, wherein the feed-through is connected to one end of the discharge vessel by way of a ceramic-containing adjustment part, wherein the adjustment part is tubular and consists of individual layers with different compositions, at least two materials A and B forming a plurality of layers of the adjustment part, these materials being chosen such that their coefficient of thermal expansion is between that of the feed-through and that of the end of the discharge vessel or at most is just outside, the layer thickness of each layer being so low that no shearing forces can occur, and the layer thickness of each layer of the same material being different.