I have a competition seating die from Redding that gives me around .003” run out or less in 243AI.
However, this is the first time that I have tried this type of die and the first time I started to measure run out.

My eyes were opened when I started to measure the reloads I had been making on regular RCBS dies. (.007-009” was the norm.) This extra run out doesn’t seem to be coming from the resized cases, it seems to come from not getting the bullet lined up correctly with the case before the die seats it. (The bullet always wants to tip over as it enters the die.)

Does anyone know the secret to getting good concentricity with standard dies?

Try starting the bullet & then rotate the case 180 & finish seating. Measure runout both ways & see if it helps. Good luck!

Check your runout on a fired case before resizing,this will give you a idea how your chamber is working! The check the case after resizing. You may have to outside neck turn you cases to get them back where the brass is the same thickness in the neck. If you have to cut the neck take very little off on the first cut and the rest on the second cut if nessary. Good Luck