Provided is a storage device for a mail-handling machine. The storage device includes a mailpiece-receiving deck along a longitudinal edge of which a referencing wall extends, and through which a conveyor belt passes for the purpose of conveying mailpieces along the referencing wall from an inlet of the device towards a sloping surface against which the mailpieces accumulate, and a skid-forming part that is supported by a structure secured to the storage device and that comes to press against said stack of mailpieces substantially over the entire length of said stack, so as to jog the top of the stack.