Check the shell width first. The cups are supposed to be tight against both sides of the cartridge. The drive side is supposed to be screwed in all the way but exposed threads on the non-drive side don't matter much as long as the BB is properly supported.There are different types/sizes of non-drive side cup so you might be able to find one at your LBS that would fit better (eg from a different model BB or one meant for a 68mm vs 73mm shell, etc).