A gas-discharge lamp (1) is described having an inner envelope (2) comprising a discharge vessel (3) and two tubular sections (6, 7) arranged on the discharge vessel, having two electrodes (4, 5) that project from the tubular sections (6, 7) into the discharge vessel (3) and that, to enable them to be supplied with power, are electrically connected to respective electrical conductors (10, 11) that extend through the associated tubular sections (6, 7) and that are enclosed in the tubular sections (6, 7) with a gastight seal along a sealing section (8, 9). The lamp (1) has an outer envelope (18) that is connected at each of its ends to respective ones of the tubular sections (6, 7) of the inner envelope (2) and that surrounds the discharge vessel (3) while leaving an outer cavity (20) between itself (18) and the discharge vessel (3). Arranged on the outside of the inner envelope (2), at least in a region or regions, is a conductive coating (22, 23) that is conductively connected, inside the outer envelope (18), to one (11) of the electrical conductors. Also described is a corresponding method of producing a gas-discharge lamp (1).