Apparatus for increasing the permeabilities of central portions of tubular wrappers which form part of successive filter cigarettes of double unit length being turned out by a tipping machine. The central portions of the wrappers include adhesive-coated uniting bands which are convoluted around filter mouthpieces in a first portion of a rolling channel for successive filter cigarettes. A perforating unit which employs laser beams is set up to simultaneously perforate the central portions of the wrappers of several successive cigarettes in a second portion which immediately follows or partially overlaps the first portion of the channel. Each wrapper can be provided with two or more annular arrays of perforations.