This idea has always been in the back of my mind, so when I made my last peep sight, I mounted on the barrel so that no matter how it reassembled the sights would be lined up with the bore. It was the only way I could be positive that a slight shift in accuracy was caused by something other than mounting the rear sight off the barrel. My inability to shoot peep sites as accurately as I should be able to, led me to try and eliminate all other causes. I use a fairly large peep, as I also hunted with this rifle and I have tried small peeps in the past with disappointing results. I see by the posting here that most feel there's no effect.Never had any shift.