I save roll ends that are too short to be used, and make a 'belt' about 5" wide. Then a piece of masking tape on one end of the 'belt' and a handle on the left over sticky end of the tape. Wrap that around the roll and stick it in place, not too tight of course. It's cheap and it has worked for me for many years. If the tape loses its stickiness over a period of time, install a new piece. Never had any problems with them. I also like Mark's idea with the Velcro, sounds interesting.
Gary