The cover for an asparagus bed has edges (3) which are folded back and sewn to the main sheet by longitudinal (7) and transverse (6) rows of stitches, forming pockets (9)for ballast. A second set of pockets (10) opens into these and has a mouth width which is at least 80% of the distance between transverse stitching, An Independent claim is included for a method for filling the pockets of the cover with ballast.