RATS!
I think I have a problem with a 0.278" Lyman sizing die ... I just tried it and noticed a problem. Instead of being tapered into the sizing portion of the die, this die is stepped from the opening diameter to the sizing diameter. I cannot reliably get the projectiles to center in the die when sizing them.
Looks to me like a machining step was missed in the manufacturing.
Is this a common way to construct smaller diameter sizing dies? Smallest one I have used before is a 0.308 or 0.309?
I went back and checked the brand of the sizing die ... it is an RCBS! Apparently Graf was out of Lyman dies so I bought an RCBS die.