In reply to StevenF:
Like most things in the mountains - it depends.
If the risks associated with dropping a tool (e.g. multi-pitch route) are significant or the nature of the climbing means a dropped tool is more likely (e.g. mixed) then I use them.
But I've seen someone take a small fall while top-roping on ice, let go of a tool placed above him and have it pull out when the elastic reached its limit. The newly-sharpened axe was then not only accelerating towards him under gravity but with the added force of the elastic. And, of course, it couldn't miss. The gash in the side of his neck was quite deep but luckily missed everything important but that was dumb luck - it could clearly have been very nasty.
So if the risks around dropping a tool aren't great and the likelihood is lower (e.g. single-pitch ice, or seconding) then I leave them off.