A faceted mirror for EUV projection lithography has a plurality of facets (25) for reflecting EUV illumination light. At least some of the facets (25) are produced as orientation facets and have a reflection surface (32), the edge contour (33) of which is oriented along two orientation coordinates (x, y) of a facet overall arrangement. The reflection surface (32) of at least one of the orientation facets (25) has a surface shape which has different curvatures along two axes of curvature (x', y'), wherein said axes of curvature (x', y') are tilted about an end axis tilt angle (α, β) in relation to the orientation coordinates (x, y) of the facet overall arrangement. A faceted mirror is achieved, the EUV performance of which is increased in particular when a projection illumination system fitted with said faceted mirror is operated for longer.