Purpose: The purpose of this paper is to suggest a methodology to calculate efficiency scores for a sample of Italian primary and middle schools. The main aim is to relate these measures of efficiency to a set of "external" factors that can affect schools' performance, such as the average socio-economic background of their students, their location in an urban/non urban setting, etc. After presenting this analysis, the paper proposes a procedure to calculate "adjusted" efficiency measures -- which take in the role of external variables -- in order to assess the "pure" management efficiency of each school, and so to avoid confusing the institution's performance with the aspects relating to its background. Design/methodology/approach: Efficiency is defined in its technical sense that is, the ability to transform inputs (financial and human resources) into outputs (results achieved by students in standardized test scores). A two-stage quantitative procedure was used to investigate "managerial" efficiency, so that the impact of external variables on educational efficiency could be suitably taken into account. Findings: The results show that the average efficiency score is quite high in the sample of schools considered, but potential savings can still be made: overall, with the schools' available resources, achievement scores could be increased by about 20 percent. Efficiency and educational equity are complementary in primary public (state) schools, and the most efficient schools are those with the lowest internal variance between the students' achievement scores; the same does not hold for middle school students' results in mathematics. Lastly, several schools appeared to be efficient when the external variables were not taken into consideration, while their background actually favored them, and they are not efficient from a purely managerial perspective. Originality/value: The most important piece of innovation is the investigation of managerial efficiency and its implications on policies. This study confirms and suggests that there could be an inverse relationship between apparent (baseline) and true (managerial) efficiency, that is, between the efficiency scores achieved before and after the "correction" made for external variables.