Recent policy studies by the Education Trust and Heritage Foundation have tried to identify "high-flying" schools--schools that help students reach very high levels of achievement, despite significant disadvantages. This policy brief demonstrates three major problems with the findings of these reports. (1) Due to questionable methodological assumptions, the number high-flying schools is significantly smaller than the number reported in those studies; (2) The numbers in these reports are being misused in a way that that understates the significance of, and need to address, socioeconomic disadvantages; and (3) these reports fail to directly address the vast amount of evidence that inequity in educational outcomes is primarily due to students' social and economic disadvantages. It is therefore recommended that: (1) Policy makers continue the recent focus on measurable student outcomes, such as test scores, but redesign policies to hold educators accountable only for those factors within their control; (2) Policy makers take a comprehensive approach to school improvement that starts in schools but extends into homes and communities, and addresses basic disadvantages caused by poverty; and (3) All educational stakeholders acknowledge that educational inequity is caused by problems in both schools "and" communities--and avoid trying to blame the problem on schools alone. (Contains 1 figure, 3 tables, and 33 notes.)