Balsa? Would.

In an attempt to cut weight on Humvees, the Army is testing models made with "fiberglass, balsa wood, foam and carbon reinforcements all held together with resin. The body of the tan composite prototype has a sandpaper feel. The fenders are pliable and can be easily bent by hand, flipping back into place when released." The 900 pounds cut from the vehicle are going to be added back in the form of extra armor and mine-blast protection.

Now I'm not too familiar with the strength of mine blasts or explosions or anything, but I do know that the last time I built a vehicle out of balsa wood the wings broke off in an hour and then the whole thing disintegrated when it rained.