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I have a Vortex 6-20x44 PST on my Howa 1500 with about .100" clearance from the front of the scope housing to the barrel. It was more like 3/8" before I changed mounts. I've noticed a significant difference in accuracy.Scope as mentioned previously is a Leupold 3x-9x Compact (later called the Ultralight and sadly now discontinued). Rings are Ruger Low (NOT what came with the gun). Had this silver one stashed, just knowing the right gun would come along. Clearance (objective bell to barre) about 3/16". Lower is better is what I believe in that regard,
At the risk of allowing this thread to become a discussion of scope height, I cannot understand how getting the line of sight closer to the bore can result in "a significant increase in accuracy" assigned to the assembly ITSELF. I trust that was not the meaning conveyed here.
Having said that, I will instantly agree that reducing the distance of the line of sight (read, "scope") in relation to the bore CAN and usually DOES result in better accuracy as a result of including the SHOOTER in that measurement. Firmer cheek weld to the comb is the first result of a scope close to the bore, making full benefit of this important interface (no pun intended) between human and machine. A better "purchase point" so to speak that can shrink groups noticeably.
We shoot better. The machine itself (scope and gun) remain at their own level of accuracy.
Nothing frustrates me more than seeing in a television show or magazine ad a scope needlessly mounted higher than it could be, carried in the field by someone who is represented as knowledgeable in such matters.