These are often used to secure a better grip on the tsuka and often feature excellent carving and design.
A second measurement is provided when a blade widens further down, such as in a leaf shaped blade.
The one problem i had and you can see it on one of the pictures is that the leather is sewn together with no glue causing the small leather flaps of the seam between the stitching to move back and forth a bit.
For example the back edge on a katana or the mid section on a diamond shaped blade.
I checked the Mekugi pins, i gave them a little tap, for curiosity, they were very snug so, I didn't bother to dis- assemble the sword as to not to disturb the really tight fit for now.