To save some space and because the old NiMH charger startet behaving strange I decided that its time for new charger. As I know what I'm doing I'm not afraid of a charger that handles LiIon and NiMH. If you don't know or care about the battery chemistry, as worst case a deep discharged LiIon could get charged (and that with a way too high current) and become unstable, so that this cell will become dangerous. Take care to not charge LiIons that are depleated below ~2.5V.
For a switching charger, the charging current is very stable. A proper CC-CV charging is applied, the charger completely stops charging when the battery has 4.22V. At lest for 24-48 hours; if you leave batteries longer than that in the charger, they get slowly charged more. After 5 days I had a battery at 4,20V while it should have dropped to 4,15V or less. So take the batteries out the chargers the day after they're full, or better even earlier. By default, the Lii-500 wants to charge with 500mA; it offers 300, 500, 700 and 1000mA as well.
Also a fast or a normal test mode is included. There the battery gets discharged and fully loaded once to measure the capacity of the cell. This take some more hours though. Discharging is done with 250mA when 300 or 500mA are chosen as charge current, and 500mA for higher charging rates. The capacity shown by the charger is very close to that I can measure with my setup.