Can anyone tell me please if a 3.7 Li-ion phone battery is of the type that has a memory and needs to be run down as much as possible before re-charging? In the past I was advised to let them run down because if you charged them too frequently, they would only use a small part of their full capacity.
Lithium-ion batteries don't suffer from the memory effect, whereby you need to discharge them fully before a recharge. They do, however, lose capacity over time (approx 20% per year) due to nature of the batteries chemistry.