Postal sorting equipment for sorting flat mailpieces, which equipment comprises a postal sorting machine having a feed inlet in which the mailpieces are placed on-edge in stacks, and a sorting conveyor in which the mailpieces are moved on-edge in series towards sorting outlets; said postal sorting equipment being characterized in that it further comprises: • a storage-tray conveyor for automatically conveying open-topped storage trays that are filled with mailpieces stacked flat; • a shuttle-tray conveyor for conveying open-fronted shuttle trays that are substantially L-shaped, and in which the mailpieces are placed on-edge in stacks; and • a tray interchanger through which the storage-tray conveyor and the shuttle-tray conveyor pass and that is suitable for automatically transferring the mailpieces stored flat in an open-topped storage tray to an open-fronted shuttle tray; in that said shuttle-tray conveyor is connected between the interchanger and the feed inlet of the sorting machine; in that the feed inlet comprises an unstacker with a fork-shaped magazine with tines, each of which is constituted by a motor-driven belt, the shuttle tray and the fork-shaped magazine being designed so that, by advancing towards the unstacker, the shuttle tray is engaged by the motor-driven belts of the magazine of the unstacker that come to be inserted under the stack of mailpieces disposed on-edge in said shuttle tray; and in that said magazine of the unstacker has a conveyor section that is mounted to move in elevation under the tines of the magazine, the shuttle tray resting on said conveyor section when it is engaged by the tines. said postal sorting equipment being characterized in that it further comprises: • a storage-tray conveyor for automatically conveying open-topped storage trays that are filled with mailpieces stacked flat; • a shuttle-tray conveyor for conveying open-fronted shuttle trays that are substantially L-shaped, and in which the mailpieces are placed on-edge in stacks; and • a tray interchanger through which the storage-tray conveyor and the shuttle-tray conveyor pass and that is suitable for automatically transferring the mailpieces stored flat in an open-topped storage tray to an open-fronted shuttle tray; • a storage-tray conveyor for automatically conveying open-topped storage trays that are filled with mailpieces stacked flat; • a shuttle-tray conveyor for conveying open-fronted shuttle trays that are substantially L-shaped, and in which the mailpieces are placed on-edge in stacks; and • a tray interchanger through which the storage-tray conveyor and the shuttle-tray conveyor pass and that is suitable for automatically transferring the mailpieces stored flat in an open-topped storage tray to an open-fronted shuttle tray; in that said shuttle-tray conveyor is connected between the interchanger and the feed inlet of the sorting machine; in that the feed inlet comprises an unstacker with a fork-shaped magazine with tines, each of which is constituted by a motor-driven belt, the shuttle tray and the fork-shaped magazine being designed so that, by advancing towards the unstacker, the shuttle tray is engaged by the motor-driven belts of the magazine of the unstacker that come to be inserted under the stack of mailpieces disposed on-edge in said shuttle tray; and in that said magazine of the unstacker has a conveyor section that is mounted to move in elevation under the tines of the magazine, the shuttle tray resting on said conveyor section when it is engaged by the tines.