Abstract: A fitted bedclothing item such as a sheet, mattress pad, anti-allergy cover, blanket or coverlet includes a top portion, side portions and end portions, and elastic segments at its four corners, stitched to edges of respective side and end portions (and to an elastic binding at lower edges thereof, if present), to provide such flexibility to its ability to fit a mattress that the bedclothing item can fit mattresses of at least two different sizes and/or thickness. The elastic segments are made of knitted or woven elastic filaments, such as SPANDEX® fabric, and can be shaped to have a straight lower edges and a curved upper portion, the curve approximating a end of a ellipse.