Purpose: This research explores the perceptions and practice of principals in schools integrating migrant and refugee children into the Israeli formal education system. The aim is to offer theoretical and methodological insights to the discourse on educational leadership. Design/methodology/approach: This qualitative (phenomenological) study used semi-structured interviews to attain a deeper understanding of the experiences of school principals as culturally relevant educational leaders. Findings: The study corroborates previous findings regarding--the need for a holistic multidimensional approach; the focus on language and communication; and the complexities and dilemmas involved in the practice of educational leadership. The study analysis revealed three central dilemmas: applying equal-opportunity and cultural diversity policies; schools as protected spaces and serving the social reality beyond the school; and full assimilation and recognition of specific cultural identity. Research limitations/implications: The research was conducted in a small number of schools and only with principals. A follow-up study could also include teachers, officials and representatives of the various organizations working with the migrants and refugees. Practical implications: Beyond financial resources, school leaders need professional (culturally responsive) guidance to support the multifaceted and complex needs of students, in part by being adaptable and flexible, and aware of the aims and practice of education for an unknown future. Originality/value: The originality-value of the present study is threefold--it explores school principals in a relatively unexplored context (the Israeli formal education system); it applies two models for organizing and analyzing research findings; and it contributes new insights on the dilemmatic nature of educational leadership.