A storage device for a mail-handling machine, said storage device comprising 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 said referencing wall from an inlet of the device towards a sloping surface against which said mailpieces accumulate, said storage device further comprising a pivot arm that is mounted to move both vertically about hinge pin and horizontally along a slide rail, on which arm firstly a friction roller is mounted for pressing said mailpieces against the conveyor belt, and secondly a holding roller is mounted for pressing said mailpieces against the sloping surface.