While rankings of presidents are quite common, rankings of Supreme Court justices are much rarer. Herein we produce such rankings to see if perceived greatness on the High Court can be predicted. We do so by examining influences that indicate historical greatness for Supreme Court Justices. To accomplish this we develop a composite greatness score of all the Supreme Court Justices based on the limited previous research on the subject. Next, we examine potential determinants of such success; the time period when they sat on the Court, the length of their tenure, status as the Chief Justice, perception of quality of opinions, and the perceived quality of their appointing president. While some past research finds (limited) evidence that great presidents choose better Justices than mediocre ones, we find that more important indicators of judicial rank are longevity on the Court, serving as Chief Justice and being recognized as an important dissenter.