I have a 30-40 Krag which is a similar cartridge, tho uses
.308 bullets instead of .311". It really likes the heavier bullets,
especially the 220 grain by Hornady. Their reps say it will work
fine on any big game, so thats what I use. Also it likes 170 grain
lasercast lead bullets which will work good for practice and small
game. Gotta handload both tho.

I would stick with the diameter made for the rifle for best accuracy potential.