This research investigates the beliefs that 14 members of the leadership team of four schools report about the strengths and obstacles present in these schools for addressing High Ability students. The qualitative content analysis of semi-structured interviews reveals two broad themes, beliefs and valuations and actions and practices. The results indicate openness about the subject, a restricted understanding of High Ability and administrative and technical obstacles to address High Ability students in the context of educational inclusion. A concerted and systematic effort that involves the entire school community is required in order to provide real opportunities for recognition and development for this group of students.