In reply to tscoobydoo: When I did it, Carrel's Gallery was an easy, totally non-serious plod across firm, well consolidated snow. Didn't need any gear at all.
I thought route-finding across the teeth was the greatest difficulty. Often you have to follow systems of ledges quite a way below the crest and there are scratches everywhere from people who went wrong. The ridge beyond the teeth is one of the most brilliant sections of Alpine climbing anywhere in a mind-blowing situation. The rock on the crest is pretty good, too. But never more than about III+. I wore crampons the whole way.
NB the slope up to the ridge just before the teeth is exposed and icy. Two tools would be better (I had only one).