The saw Bambistew posted meets all 3 even though it's bigger and heavier than I like for elk hunting.
I realize this is the backpacking forum. My favorite backpacking saw, is no saw. Best weight savings there is.
Not sure about your size limitations, it fits in a day pack no problem. It weighs about 8oz. My WY saw weighs about 20 with the sheath, Knapp saws are about 12-18 depending on model. I won't pack a folding saw unless desperate.
