A compressed coreless rolled product is described, including an inner surface defining a central cavity having an inner diameter and an outer surface having an outer diameter larger than the inner diameter. The outer diameter is at least five inches and a ratio of the inner diameter to the outer diameter is at least 0.35. Also described is a compressed coreless rolled product with similar inner and outer surfaces, wherein: a difference between the outer diameter and the inner diameter defining a thickness of at least 2.9 inches; and a ratio of the inner diameter to the outer diameter is at least 0.35. An associated method of producing the product is also described, including steps of: winding an absorbent sheet around a forming core member; removing the forming core member to form a coreless rolled product with a diameter ratio of at least 0.35; and compressing the product.