In reply to Chris Craggs:
The following are exactly my sentiments as an American using an ATC on single or double ropes. Have never not caught a fall either way.
http://www.mazamas.org/your/adventure/nw/belay-brake-hand-palm-up-or-palm-d...
Belay brake hand - Palm up or palm down?
When belaying, one always has a choice in whether to have the brake hand palm up or palm down. Both are acceptable, both are used by experienced climbers, and both have successfully caught many whipper falls over the years! Rather than debating which one is better, it’s more useful to understand the general situations in which one style of belaying may be more appropriate.
• Many climbers prefer the palm down method when belaying a top roped climber, such as when working the moves on a harder outdoor rock climb or in the gym. Palm down can give a greater degree of control over the rope when catching frequent falls, as the fist is more completely enclosing the rope when the hand moves to the braking position.
• The palm up method may be easier when belaying a leader (when the belayer may need to feed out rope very quickly) or when belaying a second from a sitting or cramped belay position. There are some who feel palm up is an easier method to teach to beginners, but both belay styles are simple to learn with good instruction.
Try both techniques, become comfortable with each, know the various pros and cons, and you’ll soon develop your own personal style and preference. By the way, never let anyone tell you one method or another is unsafe or wrong - both are fine, when properly done.