Vertical carry horseback is all kinds of problems waiting to happen. Zieg mentioned some in another post where the sheath was rubbing on the cantle (upright part behind me) which then poked the handle up into him. To us a knife is a safety device as well as just darn useful. I've personally cut horses out of 4 wrecks. The idea of getting to it with either hand is also important. Once was roping on a green colt. Caught a calf that was quite a bit livlier than the horse. He ran around behind the horse and came back up on the other side. So the rope went from the saddle horn on my right side, around my lower back and forward on my left side. Its attached to a 400lb calf that is going real fast and real hard that way. The rope has pulled me down over the saddle horn trapping my right hand so I can't pop my dallies (wraps of the rope around the saddle horn attaching the rope to the horn, normally when things go south you can just un dally, fix it and start over). I'm reaching for my knife with my left hand when I remember (this all happened really really really fast) my spur. Reach forward with my left leg, spur the horse in the left shoulder which spins him around 360 and now we're facing the calf without the rope wrapped around me. My buddy who is riding over knife in hand to cut my rope says: "You'd better start singing Kum Ba Yah." Horz carry where I can get to it with both hands is for me.