Over the past decades, many museums have seen their roles change significantly. Originally institutions essentially committed to bridging the gap between a nation's past and present, they have gradually assumed a supplementary role as social actors with a special opportunity for giving marginalised groups a chance to be heard and seen. A multitude of strong narratives, many of them traumatic, have found their way into museums, and in many ways have radically transformed the working days of museum professionals. In the wake of this development, a number of moral challenges have appeared, for instance how to deal with sensitive, contested history, how to master delicate interview situations or how to reconcile professional obligations with empathy, compassion and solidarity. The purpose of this article is to shed some light on two of these challenges. Drawing on material from my doctoral thesis, I start with a brief overview of museum and ethics, before dealing more deeply with the need to balance between individual needs with those of the greater public, and the challenges of managing individual subjectivity whilst remaining a museum employee who is expected to uphold truth and objectivity. Drawing from recent research results and practical experience, I offer some advice on what museums can and should do to respond to moral challenges.