a mercury - free metal halide high pressure discharge lamp having a transparent and gastight sealed discharge vessel and two electrodes which protrude into the discharge vessel and are arranged in the discharge vessel opposite one another , with the discharge vessel being filled with a lamp filling which has : at least one noble gas , at least the elements of iron and zinc , as well as at least one halide , with the halide comprising bromide , and with the percentage of the bromide being at least 14 mole percent of the total halogen quantity and the following relationship applying to the ratio of molar density of zinc d in μmol / cm 3 and electric field strength e in v / cm between the electrodes : 0 . 005 ≦ d / e ≦ 0 . 200 .