Alertness rhymes with:
inertness, abruptness, absoluteness, acuteness, appropriateness, astuteness, 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'