Have you ever tried one of the mini cordless saws?The mini cordless saws linked above will all be rubbish, they dont have the power. Needs to have a brushless motor to be any good.
I've used my little Stihl for up to 3-4" stuff, and it chomps through it perfectly fine. No where near as fast a decent sized saw, but it does the job, so I'd hardly call it rubbish.