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I see this quite often in different rifles/different loads.
I rule out loose screws, bad scope, hold, etc.
I support all rifles at the bench on the forearm, gentle squeeze, etc.
It just seems to come up infrequently, drives me nuts.
I sort all brass by OAL to the thousandth, all bullets to the 1/10 gr, primers from same box, mix up powder prior to measuring/pooring, then shoot a group of 4 with all these matched components.
Any ideas (too slow, too fast?)

Tracy in IL
 

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More often than not, inconsistent cheek weld causes this. Having a cheek-piece to place your head consistently goes a long way. Keeping your head on the stock through the entire group helps a lot too.
 

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Does this tend to happen at 100 yards, 200, 600? After 2 up, 2 down, do the following groups pattern more or less normally?

Based on your comments, you seem to know what most of the common causes might be and you check for them. About the only thing you didn't mention is wind flags. Can you tell us distance and tell us whether you use flags, what type, and how many. Brief, strong gusts from 12 o'clock or 6 o'clock can fairly easily cause what you're experiencing, and without flags, you may never realize what's going on.
 

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If it just happens once in awhile like KF says it may be a wind problem. If it is happening all the time it might be a bedding problem.
 

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Vertical shot disbursement, where bullets pairs up to create their own groups, so to speak.
There is a variety of elements that will cause squirrely barrel harmonics....Free floated barrels,
especially light sport weight, that allow unimpeded tones and overtones of the vibrations vs controlled
harmonics, such as bedding for adjustable forearm pressure. To crowning the muzzle with a piloted tool.

I once had a 243 that did vertical strings of around 3 inches....I added a lit'l forearm pressure and the rifle then with the same
loading put four outta five that could be covered by a dine and all five, a nickel would cover 'em at a 100 yards off of the bench.

My pre64 300 Win Mag. is a moa rifle....One morning at the range, it would not group a proven load at all. Checked
stock screws, checked scope mounting, etc... Nothing loose, not one thing amiss. I glanced at the box of fired cartridges
the firing pin strikes were off center, some primes hits off center by a lot. Jerked the bolt out, and sure enough the firing pin
hole had broken out, allowing the pin to strike the primer along the anvil leg or between them for erratic ignition.
Bushin'd the bolt face and all was back to an inch or less at a hundred yards.

If a clean bore shoots a couple high, low or off the point of aim, then will group subsequent rounds to a satisfactory level...
It sounds like a cold shot conundrum or the bore just needs a lit'l jacket material to fill the voids.

From Shilen Rifle, Inc Welcome to Shilen Rifles, Inc. FAQ
How clean is clean?
We get this question many times and have a great deal of difficulty helping some customers understand that a rifle barrel does not have to be spotless to shoot great. Many times more harm than good is done in trying to get it that way. Picture a car's fender. If the fender has a small dent in it, then professional application of body putty fills the dent. When painted over, the dent becomes unnoticeable, and the surface of the fender is smooth and consistent. The same thing happens in a rifle barrel on a microscopic level. Removing this small trace of copper puts you right back to square one. The next bullet that crosses that area will, again, leave a small trace of copper. Similar to patching a pothole. All successful benchrest shooters shoot one or more "fouler" shots down the barrel before going to the record target. This is not to warm up the barrel. They are resurfacing it on the inside. Benchrest shooters clean between relays to get the powder fowling out, not the copper. However, since copper usually comes out with the powder, they know that it must be replaced to get "back in the groove". I've had shooters tell me they "cleaned their rifle for 3 hours to get all the copper out of it." Their next statement is almost invariably that they had to shoot 4-5 rounds through it just to get it back to "shooting" again. This tells me that in order for the rifle to shoot well again, they had to replace the copper they worked so diligently to remove. I have a 7x08 Improved that shoots the same 1/2" MOA after 15 minutes of cleaning or 3 hours of scrubbing and de-coppering. Personally, I prefer shooting to cleaning. The gist of this is to set a regular cleaning regimen and stay with it. If the accuracy of the rifle is acceptable with a 15 min. cleaning, why clean longer? I would much rather have people admiring the groups I shot than marveling at how clean my barrel looks on the inside.
 
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