It's a good idea with lithium technology batteries to occasionally (maybe once a month) discharge them completely (not just until you get a warning, but until the device shuts off), then do a full recharge. Li batteries have a very flat discharge curve, so their remaining capacity can't be accurately judged by the voltage they're putting out. Battery packs have processors in them which keep track of how much current has gone in/out, and use that to estimate the remaining charge. Doing a full discharge/recharge cycle resets their memory so they can more accurately estimate remaining capacity.
The same thing should be done with a new device, to calibrate the "fuel gauge."
References:
How to prolong lithium-based batteries
Charging lithium-ion batteries