A cigarette making machine comprises means for showering tobacco onto two suction bands 610,612 to form tobacco sub-streams of similar width on the respective bands which are then merged to form a cigarette filler stream, and includes rod-forming means for enclosing the cigarette filler stream in a continuous wrapper to form a continuous cigarette rod, and means for forming or feeding onto at least one of the sub-streams, or between the sub-streams as or just before they merge, a layer 628 of core-forming material which is narrower than each of the sub-streams and is centrally located in relation thereto, whereby the core-forming material is surrounded by tobacco in the finished cigarette rod. This invention also encompasses the feeding of additional dense-ending quantities of tobacco instead of a core-forming layer.