The invention relates to a high-pressure discharge lamp with an outer envelope (1) in which a discharge vessel (11) is arranged around a longitudinal axis (22). The discharge vessel encloses, in a gastight manner, a discharge space (13) provided with an ionizable filling. The discharge vessel has a first (2) and a second (3) mutually opposed neck-shaped portion through which a first (4) and a second (5) current-supply conductor, respectively, extend to a pair of electrodes (6, 7) arranged in the discharge space (13). The outer envelope (1) has a bulb-shaped portion (2) adjacent the discharge space with a wall thickness d1. The remainder of the outer envelope has a wall thickness d2. The ratio of d1 and d2 is in the range: Formula (I). Preferably, Formula (II), the bulb-shaped portion is formed in a mold. A simplified and compact high-pressure discharge lamp is provided by the invention.