Teaching sensitive and controversial issues (SCIs) is of growing interest in contemporary, increasingly heterogeneous societies. In democracies, different groups and institutions expect their values and worldviews to be conveyed at school. On one hand, there is the expectation that SCIs should be treated neutrally. On the other hand, there are disputes over what exactly should be seen as controversial in the first place. Research on SCIs in social studies and civics has distinguished many pressures that teachers face from the very local--the community and the parents of their pupils--to curriculum policies and issues in broader social and political fields. Research on history teaching has studied ways of dealing with divergences between collective memories, and academic and lay ways of dealing with the past. The present study combines insights from both research strands. Based on interviews with Estonian and Latvian history teachers, I discern teacher positions on, and strategies for, teaching SCIs: hiding or avoiding; finding common ground or smoothing edges; just doing the job; enhancing heterogeneity and leaving the truth open. This study illustrates the complexity and multilayered nature of the challenges that shape teachers' choices and ways of coping with the various demands they perceive. Dealing with SCIs is shaped by tensions between sociopolitical, academic and educational factors and identities.