I've not seen AA or AAA sized lithium rechargeable batteries but modern low-self-discharge NiMH AA and AAA cell batteries are quite good today. The Panasonic Eneloop brand are generally widely available and good value for money. The AA size Eneloops are generally around 2100mAh and the AAA size around 900mAh.
The only downside to modern NiMH batteries today seems to be finding a good and easy to use charger which will properly discharge and/or cycle the batteries without requiring a human to fiddle with it or understand charge rates and when to discharge the cell prior to charging.
> The only downside to modern NiMH batteries today seems to be finding a good and easy to use charger which will properly discharge and/or cycle the batteries without requiring a human to fiddle with it or understand charge rates and when to discharge the cell prior to charging.
Only if you're really babying your NiMH cells is it worthwhile to do this.
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Frankly, my recommendation is to just throw away NiMH cells once they "go bad" (maybe a discharge/recharge cycle will save them, but they're really not that expensive).
For most consumers out there, the $10 trickle charge that takes 8+ hours is superior, because they'll never cycle the NiMH cells to death. How many dozens of charge/recharge cycles do you need before there's an issue, even with the most primitive of charging strategies?
When it takes months for a typical AA powered appliance to run out of NiMH charge, you realize that these "dozens" of charge/discharge cycles gives a life-span measured in _YEARS_ for these NiMH cells.
After 5 years, your NiMH cells might be on its last legs, needing a full discharge/recharge to get back to full power. Then and only then should you consider a $30 charger to perform this resurrection, except its probably more cost-efficient to just spend $2 and throw away the "old" cell.
You'll need to throw away $20 worth of cells (ie: 10 cells) before your $30 fancy charger with discharge/recharge cycles + coulomb counting is superior to the $10 crap trickle charger. Maybe an RC-car enthusiast will get there (or an electronic-hobbyist), but that's a _LOT_ of charge/recharge cycles before you reach this point. Even with the inferior $10 trickle charge design.
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EDIT: That being said, spending $30, $40, or $50 on a higher-end charger because you find it "cool" is probably worthwhile. Coolness is a factor and we're not really talking about a lot of money here. But the $10 charger + buy new cells as needed approach is probably the most cost-effective strategy.
The thing I like about the $30 charger is that it will do a discharge test and tell you how many mAh of capacity the battery has -- much better than having to figure out which battery is bad by rotating them through your bike light until you isolate the bad one.
I believe one other argument for recargeables is that you produce less junk when using them. From that view, just throwing away "bad" but potentially resurrectable cells may not be ok.
There are AA and AAA sized lithium ion rechargables, but they won't work in anything that uses alkalines, since they provide a very different voltage (3.7V). They are usually called 10440 (AAA-sized) and 14500 (AA-sized).
There are AA and AAA lithium _primary_ batteries that provide 1.5V and are in stores, but they cannot be recharged. They are far superior than alkalines in most ways, especially in the cold, but they cost drastically more, around $1-2 each. I've switched many of my low-drain applications to these batteries, where they are likely to outlast the device without leaking and destroying it.
The only downside to modern NiMH batteries today seems to be finding a good and easy to use charger which will properly discharge and/or cycle the batteries without requiring a human to fiddle with it or understand charge rates and when to discharge the cell prior to charging.