Improving weak teaching may be one of the most effective means of raising pupil achievement. However, teachers' classroom practices and the teaching "process" may matter more to student learning than teachers' observed resume characteristics (such as certification and experience). There may also be important differences in teacher characteristics across government and private schools which may help explain the large documented public-private achievement differences often found in studies. This paper delves into the black-box representing "teaching" to uncover the teacher characteristics and teaching practices that matter most to pupil achievement. This is done using unique school-based data, collected in 2002-2003 from government and private schools from one district in Punjab province in Pakistan. The data allow exploitation of an identification strategy that permits the matching of students' test scores in language and mathematics to the characteristics of teachers that teach those subjects. Within pupil (across subject rather than across time) variation is used to examine whether the characteristics of different subject teachers are related to a students' mark across subjects. The data are also unique in asking all subject teachers questions pertaining to their teaching practices and these, often unobserved, "process" variables are included in achievement function estimates. Our pupil fixed-effects findings reveal that the standard resume characteristics of teachers do not significantly matter to pupil achievement. Perversely, however, teachers are found to be rewarded with higher pay for possessing these characteristics, highlighting the highly inefficient nature of teacher pay schedules. Our findings also show that teaching "process" variables matter significantly to student achievement. There are important differences across school-types.