This study presents a corpus of turn changes between speakers in U.S. Supreme Court oral arguments. Each turn change is labeled on a spectrum of "cooperative" to "competitive" by a human annotator with legal experience in the United States. We analyze the relationship between speech features, the nature of exchanges, and the gender and legal role of the speakers. Finally, we demonstrate that the models can be used to predict the label of an exchange with moderate success. The automatic classification of the nature of exchanges indicates that future studies of turn-taking in oral arguments can rely on larger, unlabeled corpora.