The invention relates to a high-pressure discharge lamp having a single socket, comprising a discharge vessel (100) having two opposite sealed ends (120, 130) and a discharge chamber (110) disposed between the sealed ends (120, 130), wherein a first sealed end (120) extends into a lamp base (400) and the second sealed end (130) protrudes out of the lamp base (400), a first electrode (20) fixed in the first sealed end (120) of the discharge vessel (100) and having an end on the discharge side extending into the discharge chamber (110), a second electrode fixed in the second sealed end (130) of the discharge vessel (100) and having an end extending into the discharge chamber (110), and a base flange (420) disposed on the base (400) and defining a plane (421) that can be used for adjusting the high-pressure discharge lamp in an optical system, wherein the following relationship applies for the distance A from the end of the first electrode (20) on the discharge side to the plane (421) of the base flange (420) and the distance B from the end of the second electrode (30) on the discharge side to the plane (421) of the base flange (420): (I).