If you're an electronic tinkerer, and want to make a very efficient LED lamp, I suggest playing around with modern LED driver, integrated circuits (ICs).
https://www.google.com/search?q=LED+driver+circuit&ie=utf-8&oe=utf-8
The minimum voltage for these circuits might be higher than a single cell (e.g., 3 V is a typical minimum voltage for many of these circuits), but that can be managed easily enough by putting a few battery cells in series.
In simple terms, these circuits operate as a constant current source, dynamically outputting whatever voltage is necessary to produce the desired current. This is particularly advantageous to LEDs, since the LED's brightness varies more linearly with current rather than voltage. Like the Joule thief, they operate by
"switching" circuits and can output a DC current (well,
sort of a DC current) at a voltage higher (or lower if need-be) than the battery voltage, and without introducing a large amount of IR loss.
Advantages are:
- Wide range of input (battery) voltages. Without changing circuit components, you could connect three, four, five, whatever within reason, battery cells in series and it will not alter the individual brightness of each of the LEDs, nor will it greatly impact efficiency.
- Wide range of output (load) voltages. This means that you can connect one, two, three, whatever within reason, LEDs together in series, and it will not significantly affect the brightness of any given LED. The circuit will automatically adjust the output voltage such that the current through the LED chain is the desired current. [Edit: meaning you can adjust (reduce) the brightness of the lamp by merely shorting together some the output LEDs in the chain. The driver circuit will automatically compensate, and without significant loss of efficiency. (So long as the the LEDs are capable of handling a small transient in voltage, which they usually are.)]
- Usually requires a simple inductor rather than the transformer that the Joule thief requires.
- The desired current (usually the rated LED current) is simple matter of resistor value selection in the circuit design.
- Very efficient.
Similar to the Joule thief, when using these circuits ensure that the load (e.g., the string of LEDs) is connected to the circuit whenever powered on. Leaving the output open* can damage the circuit components just like what might happen with the Joule thief.
*[This might seem counter-intuitive if you're used to working with voltage sources. But with a constant current source, it's actually "safer" on the electronic circuity to short the output closed than it is to leave it open.]