Abstract: A continuous rod with a composite filler having a core constituting a small-diameter cigarette rod and a tube surrounding the core and being confined within a converted web of cigarette paper has axially spaced-apart densified sections in the core as well as in the tube. When the continuous rod is converted into a series of discrete cigarettes, it is severed simultaneously across the densified sections of the core as well as across the densified sections of the tube. If the densified sections of the core are not confined within the densified sections of the tube, a trimming device of the maker of the core is adjusted to shift the locations of the thereafter formed densified sections of the core until such densified sections register with those of the tube.