Surgical staplers include: (a) a stapler head having opposed first and second elongate jaws with opposing proximal and distal end portions; (b) a staple cartridge held in at least one of the first and second jaws, the stapler cartridge configured to concurrently deliver a plurality of parallel rows of staples; and (c) a tissue protection segment held in a proximal portion of at least one of the first and second jaws. The jaws are configured to close against target tissue and, at stapler firing, staples are delivered to a subset of tissue held inside the jaws so that tissue held by the tissue protection segment adjacent the proximal end portion of the stapler is not stapled.