Abstract: A method and apparatus are disclosed for wrapping tipping material about an assembly comprising a non-circular tobacco rod and non-circular filter plug, the assembly having a circumference less than that of a standard cigarette, on a standard cigarette tipping machine. The cigarette assembly is rolled along the surface of a rolling drum by an adjacent pressure element that is moved in the same direction as, but with a different speed from that of, the peripheral surface of the drum. The difference in speed causes the cigarette assemby to roll along the drum surface from one of a plurality of uniformly spaced-apart receiving flutes to one of a plurality of uniformly spaced-apart discharge flutes distinct from the receiving flutes. The spacing between adjacent discharge flutes is the same as that between adjacent receiving flutes, but the two sets of flutes are offset one from the other.