Cigarette tipping paper is perforated by a laser 31 emitting a beam which is directed onto the tipping paper via an acousto-optical beam deflector 33 and a beam splitter 34 producing two parallel perforation tracks 24 along the tipping paper. Each track may include a number of rows of perforations, the laser beam being deflected for that purpose by the acousto-optical device. The porosity of the tipping paper and/or the dilution of the completed cigarettes can be controlled in various ways, particularly by the use of an acousto-optical device; the latter may be used to vary the perforation pattern, the laser beam being directed onto a heat sink 52 when it is not required to perforate the tipping paper. Control of the perforation pattern, as well as allowing different patterns to be applied, is used to control the dilution factor of the finished cigarettes.