The present invention generally relates to an apparatus and a method used to upholster a box-spring frame. A textile tape with a portion encapsulating a draw cord is sewn to the inner perimeter of a border material. The other edge of the border material is sewn to a top cover material. The box-spring frame is placed within this assembly, with the top side of the frame abutting the top cover. This assembly is placed in the attachment apparatus. The attachment apparatus optionally compresses the box-spring frame and is equipped with a pair of tension applicators. Once in place, each of the two draw cord ends are secured to a corresponding tension applicator, and tension is applied to the draw cord. This tension tightens the border assembly edge around the frame. With the proper tension applied, the draw cord is secured to the box-spring frame. The bottom cover is then attached in the conventional manner with a series of staples.