Um....
I have a headlamp that normally takes 2 CR123s and contains a buck regulation circuit. I have updated the LED with a lower Vf Seoul from the old Luxeon and almost always use a single 17670 in it.
Towards the end of the discharge, it starts to dim slightly, and I am normally using the headlamp in the garage with the lights on to provide auxiliary lighting on the subjects I am working on, this means that I don't normally even notice when it starts dimming because it's just auxiliary, and the steady dimming at the end happens at just such a pace that I usually don't notice until it's like, *really* dim....
Pretty much every time I use that headlamp in the garage, I wind up discharging the cell to ~2.75V (give or take).
I've been cycling a pair of blue label protected AW cells (WAY back in the day, like from back when I first joined), in this thing for a long time now, the cells are still in pretty darn good shape. They hold a charge well, still have decent run time, stay cool during charging.. More than likely, they have done so well because I always get them to a charger pretty quickly (within 5-30 minutes) of noticing that the headlamp is "dead."
Try not to make a habit of it if you can manage it. but don't let it ruin your day either.. The cells I have been doing this to for so long have more than paid for themselves hundreds of times over.
Consider the following: Cycle life ratings for li-ion cells are based on an 80% depth of discharge (~3.7V Open Circuit), moderate to slow discharge and charge rates, 4.20V maximum charge voltages. Most li-ion cells are rated for ~300-1000 cycles. Your Tenergy cells are rated as ">500 cycles."
Cycle life is logarithmically and inversely proportional to depth of discharge. Cycle life is also inversely and logarithmically proportional to charge termination levels.
With a brand like Tenergy, we can't always trust the data sheets to be accurate, but, assuming that in their data-sheet, they suggest that the minimum recommended discharge voltage is 3.0V, based on one article I was reading recently, it suggested that most li-ion cells will take a ~66% hit on cycle life for every 0.3V below their recommended minimum discharge voltage they are cycled to...
In other words, assuming that you used the cell at perfect 80% depth of discharges through it's entire life, you might get 600 cycles before it drops to 80% of it's original capacity. Assuming that you discharged to 100% each time, (~3.0V), you might get 250 cycles before dropping to 80% original capacity. Assuming that you discharged to 2.7V each time, you might get 80 Cycles.... Discharged to 2.4V, cycle life would be something like 24 cycles....
The point being, that all of these options would technically be pretty much "OK" provided that the cell was retired at the appropriate point in it's life (80% of original capacity). The repeatedly over-discharged cell might technically be slightly more dangerous in some respects, but not severely so IMO, (since it's "shelf life" would like be so much shorter to boot, there are other factors that would not be effecting it as much)..
One could translate, and say that your 2.7V discharge was the equivalent wear and tear of 7 or 8 regular 80% depth of discharge cycles. Oops, life goes on....
-Eric