A method for the production of a mirror element (10) that has a reflective coating (10a) for the EUV wavelength range and a substrate (10b). The substrate (10b) is pre-compacted by hot isostatic pressing, and the reflective coating (10a) is applied to the pre-compacted substrate (10b). In the method, either the pre-compacting of the substrate (10b) is performed until a saturation value of the compaction of the substrate (10b) by long-term EUV irradiation is reached, or, for further compaction, the pre-compacted substrate (10b) is irradiated, preferably homogeneously, with ions (16) and/or with electrons in a surface region (15) in which the coating (10a) has been or will be applied. A mirror element (10) for the EUV wavelength range associated with the method has a substrate (10b) pre-compacted by hot isostatic pressing. Such a mirror element (10) is suitable to be provided in an EUV projection exposure system.