a squeegee blade sandwiched by a first segment of porous material on a first side and by a second segment of porous material on a second side, the squeegee blade having a projecting contact edge;

a support for mounting the squeegee blade and also the first and second segments of porous material;

wherein if the projecting contact edge is dragged in a first direction across a portion of the hard surface to which a cleaning liquid has been applied, that cleaning liquid can be thereby squeegeed off the hard surface and absorbed by the first segment;

wherein if instead the projecting contact edge is dragged in a second direction opposite the first direction across a portion of a hard surface to which a cleaning liquid has been applied, that cleaning liquid can be instead thereby squeegeed off the hard surface and absorbed by the second segment; and

wherein both the first segment and the second segment are suitable to remain essentially rigid as the cleaning liquid is being squeegeed off the hard surface; and

wherein at least one of the first and second segments has an inset area adjacent to the squeegee blade to facilitate collecting used cleaning fluid in an open pocket defined by the inset area and squeegee blade, and an outwardly extending portion more remote from the squeegee blade suitable to contact a surface being cleaned.