Shredded Paper Put in Garbage Cart Confidential Document Shredding Services available locally: Casey Moving Systems7851 Longe St, Stockton, CA 95206 | (209) 983-0417Map & Directions Pacific Storage Co523 N Hunter St, Stockton, CA 95202 | (209) 943-6683Map & Directions Shred-It1878 Industrial Dr, Stockton, CA 95206 | (209) 800-5220Map & Directions 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.