The invention relates a high-pressure discharge lamp, which comprises:an outer bulb (1) in which a discharge vessel (11) is arranged around a longitudinal axis (22),the discharge vessel enclosing, in a gastight manner, a discharge space (13) provided with an ionizable filling,the discharge vessel having a first (2) and a second (3) mutually opposed portion forming a first and a second leadthrough through which a first (40) and a second (50) leadthrough conductor, respectively, extend to a pair of electrodes (6,7) arranged in the discharge space,a lamp base (8) of electrically insulating material supporting the discharge vessel via a first (4) and a second (5) current supply conductor, each having a weld with the respective first and second leadthrough conductor, forming a first and a second current path to the pair of electrodes,the lamp base also supporting the outer bulb,the outer bulb enclosing the first and second current supply conductors,the outer bulb being connected to the lamp base in a gas-tight manner,the lamp base being provided with first (14) and second (15) contact members connected electrically to the respective first and second current supply conductors.