An absorbent article having a front waist region, a back waist region, and a crotch region extending between and interconnecting the front and back waist regions. The article comprises an outer cover, a body-side liner, an absorbent assembly between the outer cover and the body-side liner, and leg and flap elastic composites including a containment flap portion and a gasket portion. Each of the composites are attached to the liner such that one of the composites is disposed adjacent one side edge of the liner and the other composite is disposed adjacent the other side edge of the liner, each of the composites extend longitudinally from the front waist region to the back waist region, and each of the composites have a deadened portion in the front waist region or the back waist region. The article further includes a waist elastic member extending longitudinally between the deadened portions.