A wrapper for wrapping on a roll of length L having two opposed roll ends is described. The wrapper comprises an interior layer of a length Wi and of an interior layer basis weight, adapted to be adjacent the roll when the wrapper is wrapped on the roll; an exterior layer of a length We longer than the length Wi of the interior layer forming at least one end strip of width S and of an exterior layer basis weight, adapted to be outside of the roll when the wrapper is wrapped on the roll. The interior layer basis weight is different from the exterior layer basis weight. The end strip of the exterior layer is adapted to be folded on a corresponding one of the roll ends during crimping following wrapping of the wrapper on the roll.