2 inches is the smallest I will precut. Sometimes I get the bug to piece just scrappy scrappy pieces and I will use small irregular pieces. Most of the time, I put the smaller than 2 inch pieces in my dog bed pile. When I get a tshirt back that is unwanted, or fabric that no one will use, I make up a rectangle pillow case shape and fill it with my scraps. Serge the edge when its done and its off to the dog rescue. One lady there told me, they give out a bed with the dog when it goes to its forever home. I also use strips and strings for string blocks.
Check out
http://heartstringsquiltproject.com/ for more info on Heartstrings quilts or to donate blocks, quilting time or quilts.. They are a charity quilt group only.