A shrinkable material is attached to the backside of a floorcovering tile and allowed to shrink to a controlled extent to produce a backside shrinking that counteracts the tendency of the tile to warp out of plane on the floor as temperature and humidity vary during installation or while in use. The tile assumes a slightly convex shape in one or two directions that can be overcome as it is adhesively attached to the floor. The added material may also serve a secondary function as pressure sensitive adhesive, a friction layer, a fluid barrier, or a cushioning surface.