Before revision:  We contribute concrete criteria, that are easy to verify, and extended results for comparison and for existence and uniqueness of bounded solutions to BSDEs with jumps . The scope of results, applicability of assumptions and differences to related results by some alternative approaches are demonstrated by several examples for control problems from finance .
After revision:  We contribute concrete criteria, that are easy to verify, and extended results for comparison and for existence and uniqueness of bounded solutions to BSDEs with jumps , and on comparison and a priori L^{\infty .