In reply to 67hours:
I haven't used that particular axe, but I have used the Simond Fox Carving, which is absolutely brilliant. Same idea as the Gully, just without a trigrest and maybe a slightly shorter pick. Same weight, and about half the price.
I use it mainly to supplement an all-around axe on routes that demand one and a half axes. Sounds like that solution might be neither here nor there, but the Fox Carving's pick bites very well in ice, and it's perfect for steep and hard snow slopes in high dagger position.
I would happily take it as my only tool in marginal situations, like what you describe. Not optimal for self-belay or arrest by dint of its length (although actually surprisingly good!), but perfect for the odd steep section on an otherwise easy walk.