I have a futon in my basement that’s between the size of a twin and a double mattress. Since it’s impossible to fold a flat sheet around the corners (there’s nothing to tuck them into), it really needed a fitted sheet for those times when it is used for sleeping. It was easy to convert an old fitted twin sheet to the perfect size by cutting it into quarters and adding strips of fabric down the center, both length- and width-wise.
And where did the dots come from, you ask? The twin sheet had been in disuse because it had bleach stains on it. I solved that problem by appliquéing circles over the spots. (You can read my appliqué how-to here.)