New York City's elite public specialized high schools have a long history of offering a rigorous college preparatory education to the City's most academically talented students. Though immensely popular and highly selective, their policy of admitting students on the basis of a single entrance exam has been heavily criticized. Many argue, for example, that the policy inhibits diversity at the schools, which are predominately Asian, White, and male. In this paper, we provide a descriptive analysis of the "pipeline" from middle school to matriculation at a specialized high school, identifying group-level differences in rates of application, admission, and enrollment unexplained by measures of prior achievement. These differences serve to highlight points of intervention to improve access for under-represented groups. We also look at the role of middle schools in the pipeline, examining the distribution of offers across middle schools and testing for middle school effects on application and admission. Finally, we simulate the effects of alternative admissions rules on the composition of students at the specialized high schools.