Contemporary educational reforms emphasise school autonomy, performance-based management, and accountability as necessary policies for attaining improvement goals. Despite their widespread adoption, the configuration and enactment of these policies are discretionary and contingent, deeply influenced by the interaction of local contexts, organisational features, and teachers' beliefs about policy and pedagogy. Apart from these challenges, schools serving disadvantaged students, often targeted for educational improvement, also struggle with significant organisational constraints and policy overload. This study explores how disadvantaged urban schools make sense of their policy environment and engage with the school improvement mandate through different logics and practices. The analytical framework stresses the policy filtering and adaptation processes that school actors undergo when tasked with multiple implementation demands, and how these interact with school contexts to produce diverse responses. This research is conducted in Catalonia, Spain, and adopts a sequential mixed-methods strategy, relying on interviews with principals and teachers, as well as survey and administrative data. The findings are organised in four ideal types of school responses to the improvement mandate, showing the diverging ways schools engage with policy. Disadvantaged schools exhibit diverse improvement approaches despite sharing structural characteristics, explained by the interaction of contextual factors and organisational characteristics. Each ideal type prioritises different aspects, such as performance, innovation, or inclusive practices. The heterogeneity of school responses highlights the necessity for targeted, context-sensitive support to ensure equitable educational practices.