Abstract: The invention relates to a method for producing a high-pressure discharge mp, there being provided in the course of the production method a prefabricated discharge vessel (1) in which there is an enclosed ionizable filling, and in which electrodes (E1, E2) are arranged, and which has at least one sealed end (1b) and at least one supply lead (3b) projecting from said sealed end (1b), the at least one sealed end (1b) of the discharge vessel (1) having a tubular extension (1c) in which the at least one supply lead (3b) runs. According to the invention, the production method has the fabrication steps of filling glass shot (6) into the tubular extension (1c), so that the interspace between the at least one supply lead (3b) and the tubular extension (1c) is filled up with glass shot (6), and sealing the tubular extension (1c) by supplying heat.