The web of tipping paper which is being advanced in a filter tipping machine from a source to the station where the web is subdivided into uniting bands ready for draping around groups of coaxial plain cigarettes and filter rod sections is provided with projecting portions which are at least partially removed by a rotary grinding tool to provide the web with a pattern of perforations which determine the degree of ventilation of the filter cigarettes. The position of the running web relative to the tool and/or vice versa is adjustable in dependency upon one or more parameters of the finished filter cigarettes to thus vary the permeability of the uniting bands when the one or more monitored parameters of the filter cigarettes depart from the desired values.