Yeah, I'm with Archie on this one. You ususally concentrate more on the trigger while shooting one handed, your stance is different, and your hand grip placement also.
If you don't already, try shooting one handed using the same stance you use for two handed. Once you are "one track" with your one handed shooting using your two handed stance, incorporate the other "supported" hand.
I would say that stance place a key role too, but when it comes down to it, it is all about the trigger SQUEEZE.
Another question may come up, "Where the hell is the best place to put your support hand?"....that's a whole different discussion!