A method for smoothing and tensioning a fabric cover over a curved furniture frame to provide a wrinkle-free appearance. The method comprises providing a cover assembly including a fabric sheet with a sleeve and a spring steel strip pre-inserted therein, the strip having a natural bias toward a straight configuration. The assembly is secured to a curved furniture frame via upper and lower connecting means. Tensioning is achieved through the mechanical interference between the straight bias of the spring steel strip and the arcuate geometry of the furniture frame. As the strip attempts to return to its straight configuration, it exerts a continuous outward force that pushes the fabric away from the curved frame, thereby eliminating wrinkles and maintaining the fabric in a smooth, tensioned state regardless of frame irregularities.