In reply to EeeByGum:
> (In reply to Fiona Reid) Two things
> ... If you have lead a pitch facing the wall and then turn around belay, you will have up in half a twist. If, when deconstructing the belay you make another half turn the wrong way, you will have a whole twist - etc etc.
>
> Good luck
I think this is the biggest cause of the rope getting twisted. IME the simplest way to fix it is to make sure that the ropes are running untwisted when the leader sets off (I virtually always take them off belay and put them back on again to make sure this is happening and for other reasons). Then, when the second sets off from the stance they can untwist the rope, if necessary, by simply turning themselves round 360 degrees. For years I tried putting one rope over my head, or stepping over one, and it always seemed to make things worse in the end. It was a revelation when somebody pointed out the above! Turning all the way round works - obviously you have to turn the right way or you put more twists in, but it soon becomes apparent. It can make you dizzy though so watch out on small stances!
I have found that most places where you can belay, you can also manage to turn yourself round but I guess it could be tricky on a truly hanging stance. The other thing that can work if you don't have room to turn around is to untie one rope and retie it, but untying always introduces a tiny bit more risk, so could be seen as having a downside, and I think it takes longer than 'a twirl'.