Adhesive-coated bands of paper, tipping paper or plastic foil are convoluted around discrete one-piece or composite rod-shaped articles, such as coaxial plain cigarettes and filter mouthpieces, during travel through a rolling zone bounded by a pair of surfaces at least one of which moves relative to the other. The inlet of the rolling zone receives articles, each of which carries a non-convoluted band, from a conveyor which forms part of a pressing device operative immediately ahead of the inlet of the rolling zone and serving to press successively delivered bands against the respective articles and to effect an at least slight flattening of the articles immediately prior to entry into the rolling zone. The width of the path for the articles increases at the outlet of the rolling zone or immediately downstream of such outlet.