battery experts....AAAA equivalent li ion??

I'm looking for a battery equivalent (in size anyway) to a "AAAA" battery in lithium ion rechargeable. Does anyone know a model number or a website that would sell such a thing? I know I could get 6 AAAA's out of a rechargeable 9 volt but the capacity on NiCd is not good enough. I'm looking at lithium ion 9 volts as a last ditch effort.

What I really need is a battery in the 9-10mm diameter department anywhere from 50-60mm long with at least a 180mAh capacity. Ideally Id like a 3.6 vdc single battery but 2 or 3 shorter batteries that can be stacked (series voltage not a problem) to meet the height (and diameter) requirements would also suffice. ANY HELP APPRECIATED!!!

EDIT:: flexible cells are also acceptable if they can be rolled safely into the desired diameter (9-10mm)

A 9V Ni-MH battery has a capacity of only 175mAh to 250mAh at a fairly low current. Each cell's voltage is 1.2V to 1.25V for most of a discharge.

A lithium -ion battery cell is 4.2V when fully charged and its voltage gradually drops to 3.0V when its load should be disconnected. Its average voltage is 3.6V.

Li-Ion 10440 Cylindral Cell (AAA size) 3.7V, 300mAh ( LC-10440 )

It might be a bit big, at 10 x 43mm (welded tabs would add another 1 or 2 mm to length) but lots of capacity. I haven't seen AAAA.