I had this on nocks I got from Amazon, same design as nockturnals, but generic Chinese branding.
They were lose in my arrows and ruined my groups. Switched back to factory plastic nocks and fixed it right up.
I tried using a bit of paper pressed in around the lighted nocks to make them tighter and a mix of the right amount of padding did help, but I also hated how they would light up when I nocked them on my string and couldn't be turned back off without fiddling with a tiny screwdriver or knife blade in the "control hole", which couldn't be done on the string.
I have switched to Woody's Archery Group (Facebook group) nocks that fit snug by default and have an actual switch controlling the light that I can click off if I accidentally light it while nocking.
Edit: derp. I misread your problem. The nocks I mentioned are tight on my compound string, but have sufficient plastic that it can be slightly sanded to loosen up.
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