The sorting installation (1) of the invention for sorting mailpieces (6) includes sorting outlets (2) in line along a sorting conveyor (3), each outlet having a recess (4) for receiving a tray (5) in which sorted mailpieces are stored, and also a tray conveyor (8) that extends under the sorting outlets for transporting the trays filled with sorted mailpieces from the sorting outlets to a feed inlet (7) of the sorting conveyor. The installation of the invention further includes a tray-manipulating shuttle robot (9) suitable for moving along the tray conveyor past the sorting outlets, and for extracting a tray from a recess of a sorting outlet associated with it under the control of a monitoring and control unit (19) so as to transfer it to the tray conveyor.