Construction Paper Put in Garbage Ways to Reuse Use Shredded Paper as Packing Material Shipping out something fragile? Reuse your shredded paper as packing material to protect items during shipping. Did You Know? Why Shredded Paper Can Be Hard to Recycle Shredding a piece of paper shortens its fibers, which limits its recycling potential and reduces its value. Shredded paper is too small to be processed by some recyclers. It slips through sorting machinery onto the facility floor, where it gets swept up as trash.