A rewind spindle has a bearing defining a rotation axis and a main rod supported on the bearing for rotation about the axis and having an outer face forming a part-cylindrical outer surface centered on the axis and extending angularly at most about 180.degree. of the axis and an inner face lying wholly within an imaginary cylinder centered on the axis and coextensive with the outer surface. This inner face has a lower end forming an axially directed seat and an upper end. A filler rod has a lower end complementarily interfittable with the seat, an axially opposite upper end, a part-cylindrical outer surface of the same radius of curvature as the imaginary cylinder and outer surface of the main rod, and an inner face. This filler rod is displaceable when its lower end is fitted on the seat between an outer position with its outer surface coaxial with the outer surface of the main rod and lying on the imaginary cylinder and an inner position with its outer surface lying within the imaginary cylinder of the outer surface of the main rod. A link is engageable between the opposite end of the filler rod and the main rod for releasably retaining the filler rod in the outer position. Thus after winding a web up on the spindle with the filler rod retained in the outer position, the spindle can be collapsed for removal of the wound-up web by releasing the filler rod and moving same into its inner position.