A paired set of cookware lids is configured to stack on each other and on cookware items. Each lid is configured to cover the other lid, with one lid in the upright position and the other in an inverted position, making it possible to stack both lids on one cookware container, with a first lid covering the container in the inverted position, and the second lid stacked on the first lid in the upright position. The lids are provided with multifunctional rims, having a flat annular shelf an outer rim extending in a perpendicular direction from the upper side of the annular shelf, and an inner rim extends in the opposite perpendicular direction from the lower side of the annular shelf.