The present paper uses a rich dataset based on naturally-occurring lotteries for 68 new small non-selective high schools in New York City, which we refer to as small schools of choice (SSCs), to address two related questions: (1) What high school features are promising levers for increasing graduation rates for disadvantaged students? and (2) What high school features helped to produce SSCs' positive impacts on graduation rates? Our findings provide suggestive evidence that school leadership quality, teacher empowerment, teacher mutual support, teacher evaluation and feedback, teacher professional development, data-driven instruction, teacher/parent communication, academic rigor, personalized learning, and teacher/student respect are promising levers for increasing graduation rates for disadvantaged students. Our findings also provide suggestive evidence that many of these school features explain part of the total average SSC effect on graduation rates, although most of this average effect remains unexplained. Lastly, our findings indicate that SSCs are clearly distinguishable from their counterfactual counterparts in terms of school features that were emphasized by SSC funders.