Vowel harmony

Finnish has the following vowels:

Front vowels: ä, ö, y
Back vowels: a, o, u
Neutral vowels: e, i

Front vowels are, as their name suggest, sounded at the front of the mouth, and back vowels are sounded lower down the throat. A single word in Finnish either contains front vowels or back vowels, but not both (it can also contain neutral vowels). However, if two words are glued together and one contains back vowels and the other contains front vowels then ... well, you do end up with a word containing both, but it's really actually two words, isn't it?