If you want to drive a LED from a single 1.5 volt battery, there are not many options, apart from my joule thief kit. However, if that kit takes up too much space and you don't want to build it, you can use one of these brilliant little ICs.
The Zetex ZXSC380 is a tiny surface mount IC, with just three pins, that needs just a single inductor to step the voltage up to drive a LED. The ZXSC380 controls the output current so that no resistors are required.
You can either mount it on a sliver of veroboard along with the inductor and LED, or you can even just connect it directly to the LED, as I did in the photo. All you do is cut the anode lead of the LED and use the IC and inductor to bridge the gap, with the third lead of the IC connected to ground.
The only issue to be aware of with these ICs is that they are tiny, so you will need to have fairly steady hands to work with them, and SMD experience is helpful.
Datasheet is here.