Despite the importance of every nomination to the Supreme Court, a unified theory that illuminates presidential selection of nominees across the modern political era remains elusive. We propose a new theory — the "characteristics approach" — that envisions nominees as bundles of characteristics, such as ideology, policy reliability, and attributes of diversity. We formalize the theory, which emphasizes the political returns to presidents from a nominee's characteristics and the "costs" of finding and confirming such individuals, and derive explicit presidential demand functions for these characteristics. Using newly collected data on both nominees and short list candidates, we estimate these demand functions. They reveal some striking and under-appreciated regularities in appointment politics. In particular, the substantial increase in presidential interest in the Supreme Court's policy output and the increased availability of potential justices with desired characteristics has led to significant changes in appointment politics and in the composition of the Court.