See Plethoric Pundigrions1 for screen shots showing a version of Microsoft Word (I don't know which one) that for levelheaded suggests correcting it to level-headed and for level-headed suggests correcting it to levelheaded. That should give rise to a frustrating morning of trying to finalize the draft, shouldn't it?
1 Hat tip to Bob Ladd.
You will probably want to know what The Cambridge Grammar of the English Language says about what the right answer is; and those who yearn not just for authority but for actual authoritarianism will be disappointed that it reports, "It is an area where we find a great deal of variation" (p. 1760, in the section on lexical hyphens).
If you think that nonetheless an answer should be stipulated, then go ahead and make up a stipulation. What The Cambridge Grammar is telling you is that you won't have any basis for it. You might just as well have stipulated the opposite. Educated usage will not always match your stipulation (thus showing it to be a good one), and it won't always fail to match.