This article frames the intersection of the emerging fields of internationalizing teacher education (ITE) and international schooling (IS) and presents findings of a qualitative study that draws on interviews with international school recruiters to explore teacher qualities valuable for thriving in international school settings. Beyond general characteristics of good teachers, recruiters note the importance of adaptability to living and working in a foreign setting, cultural-sensitivity, and, especially, pedagogical flexibility. Additionally, recruiters discussed the significance of "fit" between the teacher and the school (and school community) as playing a role. Fit overlaps with adaptability, cultural sensitivity and pedagogical flexibility but also introduces more school-specific, subjective (and potentially parochial) factors for "fitting in." Implications for teacher education are discussed, particularly on the importance of fostering teachers' pedagogical flexibility.