A method urges a blank along an axial direction between a movable bending tool and a stationary counter-tool and, while the blank is being moved forwards, of moving the bending tool from a neutral position, in which the blank is not bent, to a working position, in which the blank is bent to the desired bending centerline radius, the working position being rotated with respect to the neutral position by a given angle of rotation depending on the desired bending centerline radius. The method further includes urging the blank between a pair of shoes upstream of the bending tool so as to make the deformation of the blank easier, and the step of moving the bending tool from the neutral position to the working position is carried out by controlling at least two degrees of freedom of the movement of the bending tool in the plane defined by the axial direction and by a transverse direction perpendicular to the axial direction. By virtue of the initial deformation of axial and radial compression of the blank due to the passage between the shoes, the following bending step by the bending tool is made easier and allows for obtaining bending centerline radiuses significantly smaller than the smallest ones obtainable with the traditional variable-radius bending methods.