I estimate the impact of attending a magnet school on student achievement in mathematics in a moderately large Southern district. Admission to magnet schools is through lotteries. Actual attendance by lottery winners is of course voluntary. I use lottery outcomes as instruments to control for bias due to self-selection of enrollees. Because lottery winners would have attended zoned schools of varying quality in the absence of magnet schools, the response to treatment is necessarily heterogeneous. Even so, these instruments are capable of identifying the effect of treatment on the treated for all students who enter magnets through the lottery. I also exploit lottery outcomes to estimate the effect of peers on student achievement. Conditional on attendance zone, a magnet lottery determines whether a student is assigned to a school with the characteristics of the magnet school or one with the characteristics of their neighborhood school. Thus, within this group, there is randomized assignment with respect to the entire set of school characteristics, including peers. This furnishes a way of identifying peer effects free of bias caused by endogenous choice of peers. Results indicate that race and income of peers have a substantial impact on achievement: the estimated difference between a school where students are 75 percent black and one in which students are 25 percent black is more than half a year's normal growth in mathematics. Further analysis indicates that these peer characteristics are not proxies for other determinants of achievement, such as teacher quality or heterogeneity in the response to treatment. (Contains 9 tables and 8 notes.)