Astuteness rhymes with:
acuteness, cuteness, abruptness, absoluteness, acuteness, alertness, appropriateness, bluntness, brightness, compactness, completeness, correctness, cuteness, directness, earnestness, eyewitness, faintness, fastness, fitness, flatness, forthrightness, gauntness, greatness, hartness, inertness, jointness, lateness, lightfastness, lightness, neatness, politeness, quietness, remoteness, rightness, robustness, separateness, shortness, softness, steadfastness, stoutness, sweetness, swiftness, tartness, tightness, unpleasantness, vastness, wetness, whiteness, witness, witness'
Astuteness sounds like:
academic, academics, academies, academy's, acceding, accosting, accusations, acquisition's, acquisitions, acquitting, acting, actinomycosis, action's, actions, acuteness, agitating, ashton's, assistance, assisting, associating, association's, associations, astonish, auction's, auctioning, auctions, augustinians, augustyniak, austen's, austin's