A method of merging postal articles (11) for delivery together with mailpieces (2) sorted in a machine (1) into relevant delivery rounds, the method comprising the following steps: entering data into the sorting machine that is representative of the delivery addresses of the postal articles to be merged; in the sorting machine, simulating an ordered sequence of mailpieces for delivery on the relevant delivery round, and, on the basis of said data, determining in this simulated sequence respective locations for said postal articles to be merged; sorting said mailpieces into sorting outlets of the machine for delivery on relevant delivery rounds, and, while each mailpiece is being machine-sorted, detecting whether said mailpiece is a mailpiece adjacent to a postal article to be merged in said simulated sequence; and responding to each said detection by inserting a separator (10) into the sorting machine so as to direct it automatically towards the sorting outlet of the machine that corresponds to the delivery address of said postal article.