Before revision: We prove the existence of bounded solutions of quadratic backward SDEs with jumps, using a direct fixed point approach as in Tevzadze [ 36 ] . Under an additional standard assumption, we prove a uniqueness result ,  thanks to a comparison theorem.
After revision: We prove the existence of bounded solutions of quadratic backward SDEs with jumps, using a direct fixed point approach as in Tevzadze [ 36 ] . Under an additional standard assumption, we prove a uniqueness result , which allows us to obtain existence and uniqueness of a solution when the terminal condition is small enough. Then, thanks to a comparison theorem.