To create lasting consensus after conflict, apologies or reparations have to be accepted by the group offering them and the group receiving them. However, findings are mixed on what determines acceptance among receiving group members, and little research has examined offering-group members. I will review data from a number of studies among different populations and issues. One theme in our research is the greater power of shame versus guilt expressions to satisfy recipients. We also show that beyond the strong role of moral image improvement predicted by Shnabel and Nadler's Needs-Based Model, offering-group members can be satisfied if the gesture is seen as fulfilling the ingroup's obligation and shifting it to the outgroup, with quite different implications for attitude toward the receiving group and toward future relations with it. A final study set against the conflict in Northern Ireland finds that while mean levels of satisfaction with a real British apology are different among offering and receiving groups, what determines both groups' satisfaction is not as different as one might think.