Better breathing = better athletic performance?

I've had asthma for more than half my life, and this winter it flared up particularly badly. I happened to hear of "breathing excercises" for asthma, and found after a little digging that there was a teacher of the Buteyko Method in our area - he came highly recommended by an alternative health practitioner I deeply respect. I went to a 2 1/2 hour introductory session this morning, and learned the basic technique. Apparently it will take quite a bit of practice, but the impacts it could have are tremendous - not just improved breathing, but better sleep, more energy, reduced allergies, stronger immune system and.. greatly increased athletic performance. He said he had one client who went from a 12 minute mile pace to an 8-minute pace after a few months. While that seems impossible and out of reach for me, if I could just sustain a 12 minute pace over a couple-mile run (and then slowly improve from there) it would be huge for me.

The basic technique is simply to breathe through your nose, all the time, in as relaxed and shallow a way as possible. There's more to it, which I'll describe if anyone's interested - I'll ceratinly report back regularly on how I'm feeling and what changes I'm experiencing, athletically and otherwise.