The consensus among education researchers is that value-added models are most appropriate for assessing the relative effectiveness of schools, teachers, or programmes for student learning. The preferred value-added model adjusts for prior achievement, but there is a variety of other specifications that may or may not include prior achievement. This paper investigates how estimates of school effects under different model specifications compare to the same-domain prior achievement model for 5 domains of student achievement. The models compared adjust for students' socioeconomic status (SES), student aptitude, prior achievement in multiple domains, and prior achievement plus student aptitude. It found that school-effects models that adjust for SES or student aptitude produce upwardly biased estimates and dissimilar distributions of school effects. Adjusting for prior achievement is sufficient to estimate school effects for student achievement in primary school, except for writing, which is less reliably measured. In secondary school, prior achievement is a sufficient control only for numeracy and spelling. The reasons for these differences between domains are discussed.