Choosing a voltage regulator for a 1.3V to 1.0V drop
You need either a buck-boost switching regulator or a low-dropout regulator. The P-type output transistor of a LDO linear regulator gives a dropout measured in hundreds of millivolts versus a much higher dropout for linear regulators that use a N-type transistor instead. They are a bit more unstable though, so be sure to read the datasheet very carefully.