Apparatus designed to cancel at least one postage or franking mark on a surface of a mailpiece moving on edge in a belt conveyor, said apparatus comprising: a conveyor portion with a plurality of small superposed belts and a plurality of superposed print heads; and control means for controlling the print heads in such a manner as to cause a print head to print one or more cancellation marks over the franking mark(s) detected on the mailpiece. Each print head is suitable for operating selectively with a plurality of superposed inkjets so as to print only a portion (¾, ½, ¼) of said cancellation mark or a scaled-down version thereof over the franking mark when said franking mark is positioned in such a manner as to be off-center between two belts.