Having regulated every shotgun I use, if I ever find one that does that it's gone as fast as I can move it. Over-convergence or under-convergence (which is a lateral issue with side by sides) can be dealt with by load testing. My last instance of proving this has been noted here in other threads but will be repeated here for emphasis. My 20 ga. Fox Sterlingworth ejector cross-fired very badly when I first patterned it, with 7/8 oz. loads at "something over 1200 fps", can't remember the exact stated velocity. Center of the patterns were 8" too far right, for the left barrel, and 8" too far left, for the right barrel. I had no idea changing loads could move it that much, and sent it to Dean Harris at Skeet's GS in OK, requesting he work his magic by honing the bore, just before the choke, to move the patterns for me. He called me and said the gun was now regulated perfectly. I happily asked how hard it had been for him to achieve this, and he said it was very easy. He just fed it some 1 oz. loads at 1150 fps and the patterns were dead atop each other. Eight inches movement at 25 yards is considerable, and this was a learning moment for me.
Happily, most guns I've patterned that have not been regulated had lateral issues, and were dealt with accordingly. Dean Harris is a genius when it comes to shotgun barrels and patterns, IMO.
