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 reduces its value. Shredded paper is almost too small to be useful to recyclers. It’s possible for shredded paper to contaminate the recycling process by slipping past the paper-making screens.