"The Li?ion can be discharged to 3V and lower; however, with a discharge to 3.3V (at room temperature), about 92–98% of the capacity is used.[2] Importantly, particularly in the case of lithium ion batteries which are used in the vast majority of portable electronics today, a voltage cut-off below 3.2V can lead to chemical instability in the cell, with the result being a reduced battery lifetime. For this reason, electronics manufacturers tend to use higher cut-off voltages, removing the need for consumers to buy battery replacements before other failure mechanisms in a device take effect."
Set up a cutoff of 3.4V, use an LDO, or a stepdown with Vin ~ Vout.