Our church cuts large rectangles from the front/back of t shirts, binds the edges of several layers together with a zig-zag stitch and sends them to Third World countries to be used as diapers.
There is a lady near where I live who makes rugs. She told me cotton knits make beautiful rag rugs. That's where my leftover t-shirt backs will go. One can only use so many rags for cleaning....
