A composite closure for an associated container is configured to facilitate gripping and manipulation by consumers, as well as handling of closures by automated equipment. The closure includes an inner closure cap, and an outer gripping layer which is applied to at least the periphery of a skirt portion of the closure cap. Notably, the closure cap includes at least one outwardly projecting element which projects to at least the surface of the outer gripping layer. In one aspect of the invention, a plurality of projecting elements are provided in the form of annular elements which project beyond the surface of the outer gripping layer along respective margins thereof, thus facilitating handling by automated equipment. In another aspect of the invention, the projecting portion comprises graphical elements which extend through the outer gripping layer for enhanced gripping and visual appeal.