Postal sorting equipment comprises a sorting machine with an unstacking member (5) and a feed magazine (7). The equipment further comprises storage trays (4) for storing mailpieces (3) and for bringing them into the feed magazine. The magazine has a deck with a first deck portion (22) that is superposed above a second deck portion (23). Each tray (4) has a bottom (26) provided with a groove that is open to the front and to the top of the tray. The first deck portion and the groove of each tray are designed to fit together so that when a tray filled with mailpieces in a stack and on edge is standing on the second deck portion, the first deck portion comes to fit into the groove in the tray under the stack of mailpieces, thereby enabling the mailpieces to be unloaded automatically from the tray.