The complexity of principals work is often characterized in terms of dilemmas. In this paper three are identified. The autonomydilemma concerns providing strong and shared leadership. The efficiencydilemma concerns leading collaborative decision-making that is efficient. The accountabilitydilemma concerns empowering local decision-making while complying with external requirements. These are explored using data from a standards framework for school principals in a large restructuring system. Judgements on what mattersin principals’ work reveal the skills, knowledge and dispositions required for principals in restructuring schools, and judgements about levels of performance are shown by how wellparticular examples of principals work are rated using a Rasch analysis. This study found what matters is that principals care for and involve others, are strong, fair and open to alternatives, articulate long-term views and balance these conflicting qualities. But, when faced with the dilemmas of restructuring, principals favour strong leadership over shared leadership, efficiency rather than collaboration, and accountability to central requirements over shared local decision-making.