Shoots better VERY dirty?

[Calif Hunter]

I have a MKI 1903 Springfield with the original 4-groove barrel. When the barrel is clean, it shoots 2-3 inch groups at 100 yards. After 20-30 rounds, though, it shoots one inch or less. The barrel looks shiny, but could it have small pits or something that "fill in" with copper after shooting it? I know about fouling shots and all that, but 20 to 30 rounds? Does anyone have any ideas or experience with this? Thanks!

 

[Herodotus]

Most likely, it shoots better after it has warmed up. This can cause the reciever to bed a little better in the stock (which would be my first guess) or it changes some relationship between the metal parts.
The rifle should shoot worse as it fouls, not better.
If tightening all the screws does not work and the barrel is decent, as you imply, then figuring out this type of problem is quite difficult. If the rifle is a collectable military rifle, you won't want to modify it (rebed of rebarrel), so this is just the way it shoots after all these years: not to bad for close up work.

 

[Herodotus]

You can also try putting a little business card shim out under the barrel near the muzzle to change the overall dynamics a little. Some times this helps, but it is pure voodoo: no one really understands what it has done.