Often a tape comes in for restoration that has been poorly wound or poorly stored. Here is an example:
One of the interesting things about this particular tape was it had been recently wound on a constant-tension professional machine prior to shipping to me.
We think that the entire tape had not been re-wound, allowing the higher tension wind to compress the inner core slightly, causing this cinching. After transferring the tape (which didn’t show much ill effect for its cinching), we still found it difficult to get the tape to wind smoothly on the reel.
Therefore, our current suggestion is if you find a tape like this, do not rewind it and attempt to clear up the cinching unless you are also ready to transfer the tape, as there are no guarantees that it can be wound better after unwinding.
Please see this post for an update (2008-02-15).