Rather than carrying a dedicated bead breaker, I carry this:
Motion Pro Assorted Tire Iron Set
A motion pro 16" tire iron. In order to get the curve of the iron closer to the bead I cut about 1/2" off the end and re contoured it.
The trick is to push down on the tire with the big iron and work a smaller iron on each side and pull up. A little lubricant really helps. Work around the tire. By the time I have gone about 1/3 the way, the bead is broken.
The added leverage of the longer iron makes it much easier and the curve aids getting the tire off the rim completely.
I carry all three irons, but 2 will do.