A combination cookvessel and cookvessel-lid-and-handle device comprising a lid main portion having an offset handle member above the lid main portion. The offset handle member having a first end adjacent to and spaced above the lid edge, a gripping portion extending from the first end and over the lid main portion, a protrusion extending toward the lid main portion and engageable with the underside of the rim and a handle-connecting portion extending between the gripping portion and the lid main portion. The offset handle member suspends the cookvessel-lid-and-handle device on the rim above the open top of the cookvessel.