An Etymological Dictionary of the German Language/Annotated/Buße
Buße, feminine, ‘penance, atonement,’ from Middle High German buoęe, Old High German buoęa, feminine, ‘spiritual and legal atonement, compensation, relief’; Old Saxon bôta, ‘healing, relief’; Anglo-Saxon bôt, English boot (‘use, gain, advantage’); also English bote (‘wergeld’), firebote, fireboot (‘a free supply of fuel’), housebote (‘prison expenses,’ then ‘a free supply of wood for repairs and fuel’), Gothic bôta, ‘use.’ Under the cognate adjectives besser, best (compare büßen in Lücken büßen, ‘to repair,’ Old High German buozzen; Anglo-Saxon bétan), will be found the necessary remarks on the evolution in meaning of the stem bat contained in these words. Compare vergüten, ‘to make atonement, give compensation’ (Ersatz); Ersatz denotes a substitute of equal worth. Compare also etwas gut machen, ‘to make good a loss,’ &c. See besser.