A mop cover has a planar main body with four outer edges, wherein a longer first outer edge is oriented parallel to a longer second outer edge, the first outer edge being longer than the second outer edge, two shorter outer edges respectively extending between the longer outer edges, the main body having at least two pockets, into which mop wings or tensioning elements can be introduced to tense the planar main body, being configured such that the mop cover can be readily gripped, and tensioned, by rectangular wings, wherein the mop cover can be guided effectively for cleaning purposes with the greatest possible degrees of freedom in corner regions, a mop cover of the type mentioned in the introduction is characterized in that at least one outer edge and/or at least one pocket are/is assigned at least one stiffening element for the partially reinforced stiffening of the main body.