Based on a multilevel analysis of the OECD PISA 2012 data on school test results for 60 countries, we have established that three presuppositions underlying the policy recommendation to introduce more choice and competition in education are untenable. First, rather than choice and competition, we find that parental voice and targets and performance measurement incentivize schools to improve students’ test results. Second, we do not find that choice and competition increase parental voice’s impact on students’ test results. Third, we do not find that choice and competition have more equal outcomes in terms of students’ test results than has parental voice. Students from high-SES families not only benefit most from parental voice, but they also benefit most from choice and competition. Overall, we do not find support for the policy recommendation to shift the balance in education in the direction of the choice-and-competition model.