A mattress covering in the form of a fitted mattress pad or fitted sheet has a top portion, an inelastic side skirt extending perpendicularly from the top portion, an inelastic underskirt extending from the side skirt, a first elastic cord attached to the inelastic underskirt at its outer periphery remote from the top portion. At least a second, separate elastic cord attached to the covering at some place between the top portion and the first elastic cord. The top portion is dimensioned to fit a...