A flat mop cover for mop-cover holder, where the flat mop cover comprises an elongate basic body. The basic body has a first elongate surface and a second elongate surface, which lie opposite one another. At least one foam-material layer is disposed between the elongate surfaces, and the two elongate surfaces are each configured to be cleaning surfaces. The two elongate surfaces are disposed such that a plate-shaped carrying element of a mop-cover holder is configured to be disposed in a sandwich-like manner between the two surfaces. The basic body is configured to absorb in a reversible manner at least four times, and at most twenty times, its dry weight in liquid, and wherein the foam-material layer has no fibers.