An axe is heavy and awfully difficult to stash in a pack. A hatchet is too small and a lot of work for anything other than splitting. A chainsaw....um..no....and survival saws are usually not up to the task of breaking down a bunch of wood. Which leaves us with an old and still the best option, a folding bucksaw. The one I like is offered by Northwest Woodsman.
The saw comes in an attractive and durable waxed canvas bag made by Frost River of Duluth, MN who specializes in making authentic back country gear using "heritage" materials and techniques with just enough modernity to make them just as useful and durable as stuff from REI.
Included in the purchase of the Northwest Woodsman Folding Bucksaw is a 24" Bacho saw blade, a solid American Hickory frame & crossbar and an aluminum tension rod with washers & wingnuts. The assembled saw is 27 inches long by 12 inches tall and when packed is a mere 24.5 inches long and 2 inches in diameter. It weighs only 1.5 pounds (including the robust waxed canvas bag) and packs easily into a portage pack or backpack.
Read More at my blog: thedamntrueexperiment.blogspot.com