A set of nestable and stackable cookware, for example, a set of pots and pans, is maintained in a stable configuration by stops attached to the outer walls of the cookware. Each stacked and nested item of cookware is supported on the rim of the lower item by two stops attached to its outer wall, on opposite sides of the item. Each stop is shaped and configured to contact the rim of the lower item in the stack at a finite number of points. A first stop contacts the lower rim at two points, and a second stop contacts the rim at one or two points. The points of contact lie in the same plane, which uprightly supports the stacked cookware item on the lower cookware item, without the walls or the base of the stacked cookware item touching the lower item.