misterE, full contact bedding just the receiver does a lot to eliminate vertical shot stringing. Then squaring up the receiver's bolt face will typically eliminate the rest of it. This assumes the barrel's stress relieved properly. Just don't have any bedding touch the barrel.
Long before epoxy bedding was available, good stockmakers would cut out the wood to have a near perfect fit to the receiver, but the barrels were still free floating. With the stock screws torqued to the same setting each time the rifle was used, there was no shot stringing in any direction. Barreled actions so fit to the stock were the best there was for even the most accurate match rifles until the 1950's when epoxies were available.
To see the improvement, be sure to test the rifle's accuracy properly. A popular method is to shoot some few-shot groups with a given rifle-ammo-shooter system then pick the smallest one to base the accuracy on. That's a bad idea 'cause the smallest groups typically happen when all the variables cancel each other out. The biggest group happens when all the variables add up in the same direction. Best accuracy happens when all the variables are as small as possible, so the best group to judge accuracy on is the largest one. If one shoots four 5-shot groups atop one another in one setting, the 20-shot composite will be bigger than any one single 5-shot group. And the smallest 5-shot group shows what the rifle-ammo-shooter does only 25% of the time. Rarely, if ever, are each 5-shot group's center's at the same place; they're scattered about the middle area of the 20-shot group composite.
US Navy Distinguished Marksman Badge 153
Former US Navy & Palma Rifle Team Member
NRA High Power Master & Long Range High Master
NRA Smallbore Prone Master
Last edited by Bart B.; January 3, 2013 at 12:14 PM.