A method for producing a high pressure discharge lamp (100) including a luminous bulb (1) enclosing a luminous substance (6) inside and a sealing portion (2) for retaining airtightness of the luminous bulb (1), includes preparing a glass pipe (80) for a discharge lamp (100) including a luminous bulb portion (1') that will be formed into a luminous bulb (1) of a high pressure discharge lamp (100) and a side tube portion (2') extending from the luminous bulb portion (1'); inserting a glass member (70) constituted by a second glass having a softening point lower than that of a first glass constituting the side tube portion (2') into the side tube portion (2'), and then heating the side tube portion (2') so as to attach the glass member (70) and the side tube portion (2'); and after the attachment step, heating a portion including at least the glass member (70) and the side tube portion (2') at a temperature higher than a strain point temperature of the second glass and lower than a strain point temperature of the first glass. Such a discharge lamp (100) and a lamp unit comprising the lamp (100) and a reflecting mirror (60) are also disclosed.
