A high-pressure discharge lamp may include a ceramic discharge vessel and a longitudinal axis, with electrodes respectively being led out from the discharge vessel by means of a feed-through via capillaries, wherein a tubular cermet part, which consists of individual layers of different composition layered axially in succession, is fitted on the capillary, each layer containing Mo and Al2O3, the proportion of Mo in the first layer facing toward the capillary being from 3 to 15 vol. % and in the last layer being from 85 to 97 vol. %, and a molybdenum cover cap, the cover cap being welded to the feed-through and the cover cap being connected to the cermet part by means of solder containing metal, and the connection between the capillary and the cermet part being established by means of high-melting glass solder or sinter-active Al2O3 powder.