Replacing a 6x6 fence post, need advice please!

I'm just replacing a 6x6 post for my fence. The previous owners put concrete around less than half of the post, and not in the ground, so it's falling over. My question was how can I avoid this? I bought an 8' post, so my plan was to bury it 2 feet in the ground, and almost fill the hole with concrete, is this a bad idea?