Lighthound has some info on li-ion sizes (approximate) for reference:
10180 battery - 10mm x 18mm (1/3 AAA size)
10280 battery - 10mm x 28mm (1/2 AAA size)
14250 battery - 14mm x 25mm (1/2 AA size)
14500 battery - 14mm x 50mm (AA size)
Max draw is hit and miss on small cells. They are generally rated really low and some have been proven to tollerate upwards of 5x their c rating, but again it’s hit and miss. Discharge curve is the only way to know for sure.
Im looking at some small Lithiums and it can be overwhelming……
I’d like to do a solitaire with a 10180 but even 350mA would run it down too quickly so it would probably have an lm317 (sot223) and resistor set to ~100mA.
fyesilova, are those GP 1/3 AA cells Li-ion or Ni-MH? I wonder if it is detrimental to the brightness on AA after using 14500. How are you charging them?