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, and a shock-absorber ramp that is mounted against the referencing wall and that is hit by the mailpieces after they are ejected from said mail-handling machine, and before they fall back down onto the conveyor belt so as to be conveyed towards the sloping surface.