How progressive is school spending when spending is measured at the school-level, instead of the district-level? We use the first dataset on school-level spending across schools throughout the United States to ask to what extent progressivity patterns previously examined across districts are amplified, nullified, or reversed, upon disaggregation to schools. We find that progressivity is systematically greater when we conduct a school-level analysis, rather than district-level analysis. This may be surprising, given the traditional view in public economics that local governments cannot effectively redistribute. We thus probe the data for explanations for this pattern, uncovering evidence that federal policies play an important role in driving within-district progressive allocations. In particular, we can explain about 83% of the within-district contribution to progressivity by the federal component of spending plus allocations that are empirically attributable to special education and English language learning programs. Our findings are thus consistent with the traditional view of redistribution being primarily the purview of central governments, operationalized in this context through mandates.