I need help with the PSP battery!

Hi,I recently just got a PSP 3000 that came with the 1200mAH battery, which to tell the truth doesn't last all that long. I was just wondering if the 1800mAH battery works with the PSP 3000 and how much longer it lasts compared to the 1200mAH battery?Thanks if you can help.P.S. I don't want to get the 2200mAH battery ( I'd like to keep my PSP ''slim'' ).I need help with the PSP battery!
I think it's a pretty straight forward equation...if 1200 gives you X hours of gameplay, the 1800 will gives you X+1/3X. So, for simplicity, if the 1200 gives you 2 hours, the 1800 will give you 3 hours. And the 2200 will give you something like 3.75 or whatever. I could be wrong, though, either in my assumptions regarding the formula or in my actual math.Anyway, the Logitech hardcase for the 2000, which also fits the 3000, is built to accomodate the 2200 battery. With that being the case, you'd never notice the extra size, as it all fits inside the case. I need help with the PSP battery!
The thing is though, i could only find bigger batteries on ebay. Ive got a PSP2000 and ive got a 2400 mAh battery and that doesnt last as long as the original 1200 mAh, even though it should last twice as long.
What everyone here has failed to notice ( although everything mentioned is good advice) is that certain functions require certain amounts of power from the battery. Browsing through you pics or media files isnt nearly as consuming as watching a movie, web surfing, or playing a large file game. It all really depends on what your doing that drains the battery slower or faster.