I have to say that one of my pet peeves is that people cannot tighten their girths or shorten their stirrups safely and quickly while mounted. I think that most people do not tighten (or at least check) their girths after riding around for a bit. I was always aware if my girth was a bit loose because I could feel the saddle bouncing a bit on the horses back. Tighten the girth and it was easier to sit the trot. 

A rider must be able to quickly adjust the stirrups without taking the foot out and while keeping one hand on the reins and it should take a few seconds only. Sure you'll have to practice to be able to do this. I used to adjust my stirrups while trotting or cantering. :-)

Anyone who feels that this might be too difficult, check out this video: http://www.barnmice.com/video/metropolitan-mounted-police

Make sure you get to the end. What wonderfully trained horses! And riders with independent seats and hands. WOW!