What type of Snaffle bit for a horse that constantly pulls down on the bit.?

He's only 4, and i have soft hands with him, i brought a straight bar happy mouth when he was 3. He's always chewing, biting and pulling down on the bit and opening his mouth. Which i feel is really getting in the way of training now and i don't want it to become a habit/problem. He needs a bigger bit anyway and i would like a snaffle. How about rollers or copper type materials? Any advice will be superb! Thanks