I had my biggest improvement (going from 18-20L/min to 13-14L/min) after someone told me to imagine I was breathing through a straw. I also got a whooping headache
After that I've found a more natural breathing pattern and have stabilized at 15-16L/min without headaches. I'm guessing I was overbreathing because of my inexperience and discomfort in the water, leading to quick full breaths as I really sucked the air from the regulator (and I have big lungs being a horn player). I think both time, experience and more comfort has helped the most, but maybe I needed to try to control my breath for a bit to realize I didn't need the huge sips of air I was taking. Still, I don't recommend controlling it too much, because the headaches are definitely not worth it.