An absorbent article (20) has a longitudinal-direction (22), a lateral cross-direction (24), an overall longitudinal article-length, an overall lateral article-width, and an intermediate portion (76) interposed between a pair of longitudinally opposed end portions (72). The article comprises a backsheet (28), a liquid-permeable topsheet (26), an absorbent body (30) sandwiched between the backsheet (28) and the topsheet (26) and at least one wing-panel (42) which is operatively connected to the intermediate portion (76) of the article (20). The wing-panel extends laterally beyond at least one lateral side edge of the backsheet (28) in the intermediate portion (76) of the article, and the wing-panel (42) is configured to wrap about an undergarment. The wing-panel includes an operative quantity of odor-control material, and at least one, laterally-outboard wing-section of the wing-panel (42) can be sufficiently sized and shaped to operatively enclose the article (20) for disposal.