Hi again,
I am still in favor of using two or three batteries rather than one with a converter.
I have done lots of tests with white LEDs and batteries and have found that there
are two ratings for a battery (this has been known for some time however)...
one rating for when the battery is used 'normally' under more typical uses like
flashlights and medium to high current draw, and another rating for VERY low
draw applications like what you would see with a white LED running with very
little current. The capacity actually comes out much higher when the current draw
is much much lower than 'normal' so the run time actually goes up again because
of that factor alone. That can get us more hours with the same battery.
If the LED is to be turned on and off in order to save even more power, then
another idea is to simply use three batteries in series and a circuit that is designed
just to turn it on and off rather than a converter. This can be made EXTREMELY
efficient, using a mosfet as the switch element of course and mosfet or lower power
microcontroller circuitry.
As an example, i have a temperature monitor using a uC chip and LED that can
run two years on two AA cells.