Given South Africa's divided past, it is imperative to improve educational outcomes to overcome labour market inequalities. Historically white and Indian schools still outperform black and coloured schools in examinations, and intraclass correlation coefficients (rho) reflect far greater between-school variance than for other countries. SACMEQ's rich data sets provide new possibilities for investigating relationships between educational outcomes, socio-economic status (SES), pupil and teacher characteristics, and school resources and processes. As a different data generating process applied in affluent historically white schools (test scores showed bimodal distributions), part of the analysis excluded such schools, sharply reducing rho. Test scores were regressed on various SES measures and school inputs for the full and reduced sample, using survey regression and hierarchical (multilevel or HLM) models. This shows that poor schools were least able to systematically overcome inherited socio-economic disadvantage. Schools diverged in their ability to convert inputs into outcomes, with large random effects in the HLM models. Outside of the richest schools, SES had only a mild impact on test scores, which were quite low in SACMEQ context. (Contains 3 figures and 7 tables.)