A method for making empty pieces of a multilayer, cylindrical tubular rod suitable for making substantially cylindrical smokers' articles, comprising the steps of: a) feeding at least a first continuous web of a first material suitable for making a first layer of a continuous, multilayer web (M); b) feeding a second continuous web of a second material suitable for making a second continuous layer of the continuous, multilayer web (M); c) forming the continuous, multilayer web (M) by superposing at least the first layer and the second layer , wherein the first layer is positioned in such a way as to occupy, in the rod , a radially inner position relative to the second layer , and feeding the continuous, multilayer web (M) along a feed direction (X); d) wrapping the continuous, multilayer web (M) around the feed direction (X), making at least a first splice of the lateral edges of the first layer and a second splice of the lateral edges of the second layer , to obtain an empty rod having a round internal transverse cross section along the feed direction; e) cutting the empty rod into empty pieces; the steps a)-e) being performed on a single machine for making a multilayer, cylindrical tubular rod wherein the step d) is accomplished by disposing the lateral edges of at least one between the first and the second layer in such a way as to make at least one between the first and the second splice as an end-to-end splice; characterized in that the method comprises a step f) of feeding a third continuous web of a third material suitable for making a third layer of the rod , wherein the third layer is positioned in such a way as to occupy, in the rod , a radially outer position relative to the first and second layers . a) feeding at least a first continuous web of a first material suitable for making a first layer of a continuous, multilayer web (M); b) feeding a second continuous web of a second material suitable for making a second continuous layer of the continuous, multilayer web (M); c) forming the continuous, multilayer web (M) by superposing at least the first layer and the second layer , wherein the first layer is positioned in such a way as to occupy, in the rod , a radially inner position relative to the second layer , and feeding the continuous, multilayer web (M) along a feed direction (X); d) wrapping the continuous, multilayer web (M) around the feed direction (X), making at least a first splice of the lateral edges of the first layer and a second splice of the lateral edges of the second layer , to obtain an empty rod having a round internal transverse cross section along the feed direction; e) cutting the empty rod into empty pieces; the steps a)-e) being performed on a single machine for making a multilayer, cylindrical tubular rod wherein the step d) is accomplished by disposing the lateral edges of at least one between the first and the second layer in such a way as to make at least one between the first and the second splice as an end-to-end splice; characterized in that the method comprises a step f) of feeding a third continuous web of a third material suitable for making a third layer of the rod , wherein the third layer is positioned in such a way as to occupy, in the rod , a radially outer position relative to the first and second layers . <EOS>