Neatness rhymes with:
completeness, sweetness, abruptness, absoluteness, acuteness, alertness, appropriateness, astuteness, bluntness, brightness, compactness, completeness, correctness, cuteness, directness, earnestness, eyewitness, faintness, fastness, fitness, flatness, forthrightness, gauntness, greatness, hartness, inertness, jointness, lateness, lightfastness, lightness, politeness, quietness, remoteness, rightness, robustness, separateness, shortness, softness, steadfastness, stoutness, sweetness, swiftness, tartness, tightness, unpleasantness, vastness, wetness, whiteness, witness, witness'
Neatness sounds like:
nading, nathan's, nation's, nations, nations', natomas, needham's, needing, neotenic, netanyahu's, netting, newton's, newtonchik, nodding, nominating, nominations, notations, nothing, nothing's, nothings, noting, notions, nutmeg, nutting