In an absorbent structure for an absorbent article, a non-woven absorbent core extends from one longitudinal end region of the absorbent structure through a central region thereof to an opposite longitudinal end region of the absorbent structure. The absorbent core has a first face, a second face opposite the first face, and laterally opposite side edges. A liquid permeable wrapsheet is wrapped about the first face, the laterally opposite side edges and at least a portion of the second face of the absorbent core to define a wrapped configuration of the wrapsheet. Tbe wrapsheet is constructed of a non-woven material and is secured in its wrapped configuration about the absorbent core at at least one securement region having a length substantially less than the length of the absorbent structure.