Use battery voltage rating or fully charged voltage?
LEDs are not really "rated" to a certain voltage, they are rated to a certain current, and their forward voltage will depend on forward current. You need to limit current through them based on the max ratings. Keep in mind, the max ratings sometimes don't mention that you need additional heat sinking to actually operate properly at those currents on some of the higher power LEDs.

If the LED is rated to 20mA, do not think it's safe to just look at (3.85Vmax - 3.4Vf - 0.55V) and use ohm's law to get 27.5 Ohms and put a resistor in of that exact value. Resistors often have "tolerances" that are ~5% unless you get fancy ones which cost more (in small runs it's not so bad, but production volume this is important). The tolerances mean you may actually be over the rating and over-stressing/heating the component without realizing it. Always be conservative, so for this case I'd go with 33Ohms 5% resistor. This means it could be between 31 and 35 Ohms in reality. This is still safe enough for the LED but will be around 16mA. Because LEDs give off light in a non-linear fashion, and because the human eye also perceives light intensity in a non-linear fashion, you will not really notice the difference between the 20mA and 16mA currents. There will be a larger and more noticeable difference between 20mA and 10mA though.

EDIT2: The current rating for LEDs is continuous - as in, forever. If you over-current pulse them most can handle very high currents for a short duration (in the microsecond range, maybe tens of millisecond range) and I have done this myself in my Strobe light project. If your LEDs are not used often, but you want a bright pulse, you can over-current them. In this case you usually use FETs and other switching mechanisms to turn them on/off for a short time, and a low value resistor is used for the pulse current limiting. 

EDIT: One final tip, is LEDs work best with constant current. For lower currents like 15,20mA you can get really cool 2-pin package JFETs (with integrated resistor) with their gate tied to the source pin which self-limits and can work with usually quite different voltage supplies. They can be found in very small surface mount packages, and will give constant current basically until the forward voltage is met from the battery being drained. You can read more about them from this Vishay app note.