http://www.surefire.com/Batteries
A bit over kill and not really designed for this application. The Li-Ion batteries in Streamlight and Surefire flashlights, along with laptops, cellphones etc really excell in high drain applications. A 20mA LED is FAR from high drain.
Thionyl Chloride Lithium Batteries - commonly found in your Energizer AA/AAA and some other sizes also excell in high drain applications. In a digital camera, you can get 6-7 times more photos on a Lithium AA as compared to an Alkaline AA because the respond better when the amerage draw is great. Put your Lithium AA in your TV remote, your performance gains are nullified, maybe 2x longer.
Manganese Dioxide Lithium Batteries - found in your button cell CR2032 or cylindrical 123's CR2's etc, also do well in high drain applications and the same rule applies as above. However I recommended the CR2032 for their relatively low cost, small size, and the fact they're often used in the application Denholm is using.
CR button cells come in a variety of sizes. Some of the smaller ones being CR1025, 1216, 1220 and largest ones being in the 3032 range. The battery number is also its dimension. A CR 2032 is 20mm in diameter and 3.2mm thick, while a 1025 is 10mm in diameter and 25mm thick.
I'd probably shop ebay or online to get these cheap. Your local retailers will charge $3-4 on average for a CR2032. Ebay, I found them a 10 pack for $2.50 w/ free shipping. At this price, its really close to the cost of what these cells actually cost in bulk.