A myth buster about draining the battery 1st before fully charging it:
"Unlike Ni-Cd batteries, lithium-ion batteries should be charged early and often. However, if they are not used for a long time, they should be brought to a charge level of around 40% - 60%. Lithium-ion batteries should not be frequently fully discharged and recharged ("deep-cycled") like Ni-Cd batteries, but this is necessary after about every 30th recharge to recalibrate any external electronic "fuel gauge" (e.g. State Of Charge meter). This prevents the fuel gauge from showing an incorrect battery charge."
So basically, recharge it frequently, but every once and awhile drain it completely and recharge it back to full.