In some embodiments, methods for ligating nucleic acid ends comprise: conducting a nucleic acid ligation reaction in the presence of at least one agent that generates a ligatable terminal 5′ phosphate group by removing an adenylate group from a terminal 5′ phosphate of a nucleic acid. In some embodiments, an aprataxin enzyme can catalyze removal of an adenylate group from a terminal 5′ phosphate of a nucleic acid. In some embodiments, methods for ligating nucleic acid ends comprise: conducting a nucleic acid ligation reaction in the presence of an aprataxin enzyme under conditions suitable for ligating nucleic acid ends.