GunnarGG is right - is that "Ultrafire", "Trustfire" or Xxxxfire 880?
These are junk brands.
Their actual capacity underlies their huge ambit claims.
Because in CR123 or 16340 size rechargeable, nothing is bigger than 750 mAH capacity at the current technology level.
For your RRT-0 with a 16mm battery barrel diameter, buy yourself an AW RCR chemistry, 16340 size, 3.7V, 750 mAH capacity, with Protection Circuitry.
For your RRT-01, this is a newer design, so it has been bored out to 18mm diameter barrel, rather than just 16mm, so buy yourself an AW IMR chemistry, 18350 size 750 mAH capacity battery.
The IMR chemistry has less internal resistance, to output more amperage, so the RRT-01 can deliver some 550 or even 600 lumens, but the IMR chemistry, despite its extra diameter, has only just caught up to the smaller conventional RCR chemistry 16340, for 750 mAH capacity.
An IMR chemistry in 16340 size only has a puny 550 mAH capacity.
Also, the IMR chemistry does not have any protection circuitry, so once it flashes or auto shuts down, do not keep on trying to use it - recharge it immediately.
Continually trying to use an already flat IMR chemistry will drain the voltage out, and cause it to permanently fail.
Both types and sizes of batteries can be purchased from AW himself in the CPF MarketPlace at:
http://www.cpfmarketplace.com/mp/showthread.php?230876-AW-s-LiIon-Batteries-Sales-Thread-*Part-12*
Be sure to create a separate password for the CPFMarketPlace...