Improving schooling by reducing achievement gaps based on family background has been on the agenda of school governance worldwide for more than three decades. International benchmarking like the OECD's Programme for International Student Assessment (PISA) is used to find models of best practice in effective school governance. Enlarging school autonomy, strengthening school management, and enhancing accountability have emerged as widely recommended and globally spreading governance tools. However, we do not know how much these tools make a difference between schools. To close this research gap, we conduct a multilevel regression analysis, which explores the association of student and average school socioeconomic status, migration background, school disciplinary climate and governance tools with student PISA scores. The United States, Canada, South Korea, and Singapore in 2009 and 2015 serve as test cases. Our findings indicate that school governance tools do not reduce achievement gaps.