Hello MMD and Don Teach.  Whenever I put a length of tape along one
edge of a roll, I always put an equal length along the opposite side,
even if that side is in perfect condition.  This avoids a re-rolled
roll whose diameter is larger on one side compared to the other.  A
roll like that would surely experience stresses liable to stretch the
paper.  Rolls with extensive taping along the edges feel rather squishy
in the middle, after re-rolling, because of all the air spaces between
the turns.

On rolls that are in good condition, with little or no tapeing, I use a
"Ponytailer" hair band to stop them unrolling in the box, unless they
are Aeolian rolls with a string tie.  However, if they are extensively
repaired, I use a length of 6 mm (1/4") black cotton tape as a tie,
because one can pull the tape just tight enough to retain the roll
without squashing it in the middle.

White tape would do just as well; I think that black looks classier.

John Phillips
Hobart, Tasmania