The aim of this study was to characterize those schools in the Autonomous Community of the Basque Country (Spain) with high numbers of immigrant students in accordance with their effectiveness level (high or low). Three effectiveness criteria (scores, residuals, and times) were used to select the schools, resulting in three models: a ceiling or floor effect model, a contextualized cross-sectional model, and a contextualized longitudinal model. Of the 524 initial schools analyzed, 7 were found to have high or low effectiveness levels and higher-than-average immigration levels. Following the selection, the discourses of 40 education stakeholders were analyzed through semi-structured interviews and discussion groups. The results highlight the strong sense of vulnerability felt in some schools, as well as the general conviction that greater support, commitment, and stable, collaborative leadership by the management team and inspectorate would contribute to improving effectiveness.