A fastening 11 for an elastic band 12 comprising an attachment for a first end 12a of the band and a cleat 14 comprising a cleat slot (15, fig.1) into which a second end 12b of the band can be jammed. The fastening may have a flat base 16 having a base slot 17 comprising the attachment for the first end of the band, and two posts 18 upstanding from the base that define a slot adapted to receive and retain the second end of the band. The slot preferably extends at right angles to the flat base, and widens where it adjoins the base. The slot may have a triangular shape where it widens. Preferably, the base is elliptical in shape. Also claimed is an elastic band in combination with such a fastener. The band may be in the form of a tourniquet.
