Take one of the teeny-tiny button compasses [...]
I'm not enthusiast about putting so much faith in a single device. particularly when it is a device that is dependent on batteries and one that is relatively delicate. Count on a cell phone for communications, timekeeping and compass and you lose the who;e shooting match if the cell phone falls into a mud puddle.
My preference is a small, and very durable, button compass. The best of them have survived being swallowed and retrieved at the other end. A testimate to durability but otherwise a pretty useless bit of information unless you anticipate a prison camp and strip search in your future.
The real deal:
http://www.bestglide.com/FB1605_Info.htmlIt is pricy at $36 but as long as you don't lose it one should last a lifetime.
Very good:
http://www.bestglide.com/marbles_brass_compass.htmlPerfectly usable and almost as tough for less than half the price.
A bit larger:http://www.bestglide.com/brunton_compass.html
Dirt cheap but rugged enough and small enough to stuff into any kit or hide until needed in a jacket pocket. A selection of small workhorse compasses for cheap.