For alpine trips that are expected to be free of snow and ice, what `just in case’ gear do you bring for unexpected crossings of icy couloirs?
I sometimes encounter this situation in late summer in the PNW or Rockies after incorrectly guessing that all the snow and ice will have melted out. Usually the couloir is only a few yards wide, and I simply want to cross it rather than climb up the couloir.
At present I only carry an axe and chop steps, but my boots/rockboots give very little traction on hard, late-season ice. I generally don’t have a rope for sub-5th-class routes.
Would there be much benefit to additionally carrying instep crampons or other lightweight traction devices? Or are they useless in this situation?

