The word unkempt (untidy, dishevelled, slovenly, uncombed) is common enough, but kempt (tidy, neatly kept, combed) is much less so. I’m not sure why: it is itself a neat word, expressive and economical. Here’s an example from Denis Johnson’s great war novel Tree of Smoke:
At this point Jimmy Storm took notice of a patron sitting down to another table, a rather tall young Asian woman, prepossessing, strikingly kempt, sheathed in a glamour of silk . . .
Most sources say kempt is a back-formation from unkempt, which has been around for centuries. In Middle English unkempt took the form unkemd – from un- + kembed (or kempt), past participle of kemb “to comb”. Comb gradually replaced kemb except in isolated dialectal use.
We find kemb in Chaucer: “His longe hair was kembed behind his back.” In Old English it was cemban; the American Heritage Dictionary says this is derived from the Germanic form *kambaz, originating in the Indo-European root gembh- “tooth, nail”.
Jack Winter’s comical essay How I Met My Wife is full of unusual and improbable words created by removing negative prefixes, and sure enough he makes use of kempt: “Her hair was kempt, her clothing shevelled, and she moved in a gainly way.” Various poems exploit the same terrain.
But kempt, as we’ve seen, can also be used with a straight face; contemporary examples may be browsed at Wordnik, many of them in the compound adjective well-kempt:
On the whole, she was not much cleaner or any better kempt than the ragamuffin boy. (Margaret Peterson Haddix, Uprising)
With his thick gray hair, salt-and-pepper beard, and aviator glasses, he looked like a well-kempt Jerry Garcia. (Paul Elie, ‘The Velvet Reformation’)