I've pieced backs a number of times, and our ancestors definitely did, too. I like LoisM's idea of cutting your fabric in half to use on each end. You can put a different fabric in the middle, or put some other larger blocks into the section in the middle for extra interest. I also like the idea of cutting your fabric into strips (wider ones) and alternate with strips of other fabrics in colors similar to the front -- that way you have a reversible quilt. Instead of looking at it as solving a problem, make it a creation you can have fun with.