The ability to improvise is a really critical component of your first aid training, and hence your kit. I always carry a bandanna which can serve as a triangular bandage (because of this potential use I try hard not to use it to blow my nose). The stays in your pack can form the basis for a splint ( I have drilled holes in the ends of mine in preparation for this - saves weight, too).

On one very interesting encounter while on a recreational climb, we fashioned a cervical collar from a blue foam pad and tape to stabilize our victim. It worked fine.

Look at all your gear and think of how the items you are carrying can serve for victim care. Since you almost always want to treat for shock, the ability to supply heat and retain a stable body temperature means your stove and sleeping bag, tarp, etc. will often come into play.

One of the most useful things I ever did in a First Aid class was to tell the students to fetch their packs and see how we could improvise in the face of various scenarios. I learned a lot myself.

Your attitude is important as well. In most wilderness situations, you are going to be with the victim a lot longer than urban situations, a reasonably upbeat, positive demeanor helps the victim.

I have never applied a tourniquet, or seen one applied, for real, in more than 300 emergency scenes, including one amputated arm and several gunshot wounds. I queried a good friend, who had been working as a paramedic for about a year, about this. He had never used a tourniquet, either. Battlefields are a different situation - one reason I have never applied a tourniquet may be because the victim had bled out and expired by the time we arrived on scene - there is usually a lapse of at least an hour or two between the incident and the arrival of SAR personnel. Just another reason why a wilderness traveler should have training in first aid.