Last weekend I went on my first backpacking adventure and spent three days on the Ice Age Trail with some good friends who are experienced backpackers:
Given the fact that I am a member of this EDC forum, and as such very prone to “over-packing”, going lightweight was an internal challenge for me. As such, I packed my trusty Delica, a Leatherman Wave, and a SAK Classic. Despite all I have read regarding backpacking and a minimal need for carrying a knife when on a trail, I managed to find a reason to use each of these items. 
However, on the coldest night, we decided to make a fire to warm up a bit. As we sat in a circle trying to break down wood into more manageable pieces I found myself with an intense desire for a knife I could baton with which would have expedited the process immensely. I have only a few fixed blade knives, and would not trust any of them for this purpose. So, I am looking for recommendations for a fixed blade backpacking knife to add to my kit.
This is my wish list:
– Small/light weight, but still able to get through a smaller piece of wood (the max diameter I could break with leverage).
– Budget friendly, I could throw out a number, but we all know that I would likely spend more anyways. 
– Multi-use, ideally this would allow me to leave the Delica at home.
I am open to any suggestions, recommendations, etc. Thanks guys!
– Massen