The invention relates to an assembly of a capped high-pressure discharge lamp (1) and a lamp holder (50). The discharge lamp comprises an outer envelope (10) in which a discharge vessel (11) is arranged. The outer envelope has a pinched portion (20) provided with a clamping member (25). A lamp cap comprises a substantially circular-cylindrical cup shaped portion for receiving the clamping member and is provided with a protruding collar (36). The lamp holder (50) comprises a substantially circular-cylindrical flange (55) for receiving the cup-shaped portion such that the flange engages the protruding collar. An inner diameter of the flange (55) has a tolerance of less than or equal to -0.2 mm. An outer diameter of the cup-shaped portion (33) has a tolerance of less than or equal to +0.2 mm. The respective tolerances extend over a length of at least 2.5 mm, measured with respect to the protruding collar.