While developing a method for reasoning about programs, Pitts defined the [top ][top ]-closed relations as an alternative to the standard admissible relations. This paper reformulates and studies Pitts's operational concept of [top ][top ]-closure in a semantic framework. It investigates the non-trivial connection between [top ][top ]-closure and admissibility, showing that [top ][top ]-closure is strictly stronger than admissibility and that every [top ][top ]-closed relation corresponds to an admissible preorder.