U.S. Patent 5,645,087 assigned to Hauni Maschinenbau AG, Hamburg, Germany. Fragments of plastic fibers, such as cellulose acetate fibers, forming part of mouthpieces of filter cigarettes or like rod-shaped smokers' products tend to become separated from the respective filter mouthpieces at the end faces which develop in response to the making of cuts across filter rod sections of double unit length between pairs of plain cigarettes to obtain filter cigarettes of unit length. The fragments of fibers which tend to become separated and to contaminate the area around the filter cigarette making machine are either bonded (e.g., by heat and/or by a solvent) to the respective mouthpieces, or are removed by suction and/or by resorting to electrostatic precipitation. It is also contemplated to cause smoke-permeable layers of filter material to overlie the end faces of the mouthpieces.