An installation for shaping an axisymmetric fiber preform presenting a profile that varies in radial section, includes a storage mandrel for storing a fiber texture in the form of a wound strip, one or more follower rollers, and an axisymmetric mold on which the fiber texture is to be shaped by being wound, the follower roller(s) being placed between the storage mandrel and the axisymmetric mold, the installation including at least one tension adjustment device for adjusting tension on the fiber texture, the device including at least one row of rods aligned in a first direction parallel to an axis of rotation of one or more follower rollers; each rod presenting an endpiece at a free end in order to come into contact with the fiber texture.