'LED bulb' for 2.4 Volts:

I use the E10 base LED lamp below for caving. A very popular headlamp is the FX2, but it is based on 2 NiCd cells, so only 2.4 Volts.

I designed a tiny circuit wit 2 transistors to be fitted into to E10 base, so its a real plug-and-play replacement!

It works fine from 1.0 V, and is optimised to deliver 25mA per LED at 2.4V. Input current is around 130mA @ 2.4V for 3 LEDs

For the schematic see below. All parts are SMD (0805 & SOT23). The inductor is from coilcraft. Both transistors may also be BC847 without sacrifying efficiency too much.

You can build it together by using the inductor as carrier.