In a short-arc high-pressure discharge lamp (1) with a xenon fill for digital projection purposes, the separation L in mm of the two mutually facing end sections (6a, 8c) of the cathode (6) and the anode (8) when the lamp is hot is given by the relationship 0.8nullPnullLnull1nullPnull1, where P is the lamp power in kW. Further, the diameter D of the circular-cylindrical middle section (8a) of the anode (8) in mm obeys the relationship Dnull2.1nullLnull10.