Riding without stirrups?

I'm not exactly sure how this is happening. I do the exact same thing and my reins never get caught in my stirrups. Are you tucking the loop left over underneath the rein between your hand and the bit (sorry i can't think of a better way to say that right now)? The only other thing I can think of is to just take the stirrups off for those ten minutes. It actually makes a big difference (the buckle and stirrups is in your way a lot more than you think) but it is a pain to take them off and put them on....