Hi Butter,
Its already been done.
Go to www.energizer.com and click on Technical Info. Choose the battery chemistry (alkaline?) that you are interested in and select a battery (9V?)for its spec's and test results.
Look at their new Lithium AA cells and the 9V medical one. They seem to last forever and just keep going and going and.... like their bunny ads.
Also look at their Ni-MH rechargeable cells. Each time I look they have a higher capacity. They also have a very good tutorial about chargers.
Compare the capacity of a 9V battery and 2 AA cells which are nearly the same size. The AA cells cost a lot less but produce nearly 4 times as much power. Convert your circuits to work at 3V like I did or use a simple voltage-step-up IC.