Why can't I adjust the flapper on my toilet so it flushes correctly?

Ok, so my husband and I just bought a house. The upstairs toilet always had a little trickle to it. We replaced the flapper and the trickle stopped. Problem is, no matter how I adjust the chain, it will not flush right. If the chain is too long, you have to hold it down for it to flush, and when I shorten it, it will flush, but the tank NEVER completely empties, and then the flapper won't seal all the way. I have tried every length imaginable on this chain and I don't know what else to do. Any ideas?