Seat back with adjustable headrest

A piece of furniture has a seat back having a front face and a headrest having a front face and positioned above the seat back with the front faces both facing forward. A guide forces displacement of the headrest relative to the seat back in a continuous and synchronous tipping/sliding movement between a lower position with the headrest relatively closely juxtaposed with the seat back and with the front faces generally parallel and an upper position with the headrest spaced above the seat back and the front faces forming a large acute angle. An upholstery cover is stretched as a single piece over the front faces of the headrest and the seat back.