... I am a bit disappointed about M1 carbine accuracy. Paper plate size groups - that is really disgusting news. Anybody knows any special trick that will improve M1 carbine's accuracy?
I can't speak from experience, but I discovered this bit of info in my files. I foolishly didn't note the source, but FWIW:
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Re: .30 Cal. M1 Carbine Accuracy
From: B. Jackson
Date: 12 Jun 1999
...There are a few things you can do that may tighten down the groups your Saginaw shoots. Loosen the front band, slide it forward and remove the handguard. Pull the barrel and action up and out of the stock and inspect both closely for any sign that metal is rubbing on wood. Check for wood/metal points of contact in the short barrel channel. If the barrel is contacting it on the sides or bottom you will see matching lines on barrel and stock where they touch. Contact in the barrel channel can open groups up as the barrel warms, expands and increases pressure at that point. The group will tend to shift, or string away from the contact point, eg. contact at 4 oclock on the barrel will string bullet impact toward 10 oclock on the target. Relieve just enough wood so the barrel and stock don't touch each other.
Holding the assembled action in the stock with the handguard off, look down from the top side of the barrel as you cycle the operating slide and bolt fore and aft. If one or both sides of the op slide are contacting the inside surface of the stock, relieve those high spots in the stock. Rub in some boiled linseed oil on those spots in the wood that needed sanding. Make sure both front and rear sights are solid and not moving due to a poor fit, damage or staking punch points that have loosened over the years.
One simple modification that made my Carbine shoot tighter groups involved the fit between the recoil plate in the top rear of the stock (above the grip) and the recoil lug on the rear of the receiver. Ideally, there should be enough upward tension between the recoil plate in the stock and the lug on the receiver to hold the barrel up out of the barrel channel approx. 1/2" - 3/4" when the action is fully assembled and placed back into the stock. To obtain the correct fit and tension with my Carbine, I glass bedded the recoil plate in the stock (plate, bolt and nut liberally coated with release agent), put the action into the stock carefully seating the lug inside the plate while holding the muzzle up at approx. a 20 degree angle above the barrel channel, (that's about 15º above where the barrel would seat into the barrel channel). I had placed a piece of packing tape (blue painting tape would work even better) over the barrel channel so it would center the barrel in the channel while still keeping the bottom surface of the barrel even with the top edge of the channel (approx. 1/2" or so). The trick is to lower the barrelled action slowly back down to the tape where the weight of the action and barrel is supported by the tape and centered over the barrel channel in the stock. (Sounds more difficult than it is). Once the action is so aligned and barrel rested against the tape, simply tighten down the recoil plate bolt until you notice the first sign of increased pressure by the underside of the barrel against the tape holding it above the barrel channel in the stock. Stop there and let the bedding cure for at least 24-36 hours. Then remove the action from the stock, trim away any excess bedding that may have oozed around the back side of the recoil plate and forward into the stock or onto the rear of your receiver lug. Once cleaned up, put the action back into the stock and you should be rewarded by seeing that there is a modest amount of upward tension that must be overcome as you push the barrel gently down into the barrel channel. Put the handguard in place and seat the barrel band to lock it all together, DO NOT tighten the barrel band screw down as far as it will go.
The next step is very important to getting the improved accuracy hoped for. Take your best ammo, get on a bench at the range in calm wind conditions and just get on paper at 100 yards so you can compare groups (of at least five shots) with the barrel band screw turned down three HALF turns from its full "out" postion. Shoot another group at 5 half turns down, another at 7 and another at 9 half turns down. If 7 is tighter than 9, go back to 7 and shoot another group. Continue to shoot groups until you "fine tune" the barrel band tension and settle on how many HALF turns down give you the tightest groups. Then write that number down or memorize it for life. My Carbine shot optimum groups at 7 half turns down, but each Carbine has different dimensions that will vary this number. This simple modification has improved the groups of every Carbine so "tuned". Of course you want to start the whole process by giving the bore and the chamber a very thorough cleaning. Use plenty of good solvent, a bronze brush, cotton patches and JB bore paste or Remington Bore Cleaner to remove what may be many years of powder and copper fouling in the bore. Be sure to turn the action sights down while cleaning so none of these solvents and cleaners migrate down into the gas port and gum up the gas piston. Be careful to protect the crown at the muzzle by using a good coated rod (Dewey) and guiding it carefully into the muzzle so no damage is done to the end of the rifling.
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This won't magically make it a perfect deer rifle, of course.

Stuart