The present invention relates to a cover (10) made of fibre material, in particular made of fibre material with cellulose fibres, for at least partially covering an opening (30) of a container (28), having a dome portion (12), which is intended to cover the container opening (30) at least in part, and having a fitting portion (14), which outwardly encloses the dome portion (12) at least in certain sections, preferably in full, and is intended to fit the cover (10) on a mating fitting portion (26) in the region of the opening (30) of the container (28), preferably at a periphery which bounds the container opening (30) of the container (28), wherein the cover (10) is formed at least in certain sections, preferably in full, from a single-constituent material, wherein the cover (10) of the container (28), within a section (12, 14, 20, 24, 32, 38, 40) of single-constituent material composition, has different material properties in different regions.