A cigarette-making method is provided, comprising forming an elongate tobacco rod having a non-circular cross-sectional shape and opposed ends, by circumscribing a tobacco charge with a wrapping material. A filter element is formed having opposed ends and a non-circular cross-sectional shape corresponding to the cross-sectional shape of the tobacco rod, by circumscribing a filter material with a plug wrap material. One end of the tobacco rod is axially aligned and abutted with one end of the filter element, and a tipping material is applied about the tobacco rod and the filter element, wherein the tipping material extends across the abutting ends thereof, so as to join the tobacco rod with the filter element and form a cigarette having a non-circular cross-sectional shape along a length thereof. Associated apparatuses and methods are also provided.