A good example is the verb 吃 chi1 "eat". Add 完 wan2 "finish, complete" and you get a compound roughly equivalent to English "eat up". With 飽 bao3 "full", 吃 expresses the meaning of "eat until full". If you 吃飽 your meal, the implication is that, like Mr Creosote, you really couldn't eat another bite, whereas 吃完 simply means that you're finished eating (perhaps because you had the misfortune of sitting near Mr Creosote).

How's that compounding? Seems to me that the neutral hypothesis would be that 完 is a syntactic aspect marker, but of course, I don't know any Chinese.