School district budgets typically hide as much as they reveal. Superintendents are finding this as they discover huge deficits that nobody saw coming. District budgets are opaque by design, and they often mask important facts about resource allocation within a district, as well as about total spending. This paper reports the results of an original study of district spending at the school level. We computed real-dollar school budgets, based on actual staff salaries, and found huge within-district variations in per pupil spending. These differences were largely driven by differences in teacher salaries. Under collective bargaining agreements, senior (and higher-paid) teachers are allowed to avoid troubled low-income schools and cluster in schools serving more advantaged populations. Lower-income schools therefore must hire many new and low-cost teachers, who themselves leave as soon as they gain seniority. District budgets cover up the resulting differences in real-dollar spending via teacher cost averaging, assuming that every teacher costs the same. Based on original research in four districts, we show that teacher cost averaging drives significant amounts of money (several hundred dollars per pupil in many cases) out of schools serving poorer students and toward better-off schools. When applied to teachers employed by federal programs such as Title I, teacher cost averaging also means that less is spent on program services than reported, and some federal funds leak into schools that are supposedly not eligible for them. Lower than average spending on teachers is surely not the only problem faced by low-income schools. But the fact that such schools subsidize higher salaries for teachers from elsewhere certainly reduces their opportunities to stabilize programs and improve instruction. We suggest ways districts, states, federal policymakers, and parent-litigants might address the problem. (Contains 6 figures, 1 table, and 18 notes.)