Here are links (amazon.com) to the pocket chain saws that I'd mentioned earlier. They are NOT wire-type saws, but rather narrow versions of a typical chain saw.
http://www.amazon.com/Unbelievable-Pocket-Chain-Portable-Camping/dp/B0002YPMSY 
http://www.amazon.com/Pocket-Chainsaw-Survival-Tool-Carrying/dp/B000LNQA50They're both made by the same company.
If your life might depend on it I think I'd go with the second one - with the large loop connectors that could be used even if the cordage snapped and a storage can.
They cut amazingly fast - and if you hold it in an arc (around the branch) it essentially cuts three-ish sides at once.
The only thing to be careful of is - like with any other saw - future movement of the kerf that will pinch the saw blade. Its easier to do when cutting in a arc.
I've only used my pocket chain saw a few times, so I haven't a clue how long it will stay sharp.
Like I said before, my preference is to use a "real" folding saw rather than these. There are several excellent versions available.
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