Yeah, the umlaut* is absolutely essential over "reëmphasized" vowels (and when you want to be fun and archaic in Dutch: mijn -> mÿn...). Words like coöp, coördinator, and the like always come out a bit strange unless there's an umlaut or a hyphen-- and I'm of a mind to absolutely minimize use of hyphens in English.

* Actually it's "dieresis" in this context (i.e. separating vowels which'd otherwise be part of a diphthong). "Umlaut" is the fun sound change that happens with German vowels using the same symbol. How geeky must I be to know this crap?

Post Scruptum: Add "separate", "independent", "consistent" to that list of A/E words...