Does racial and gender diversity on the federal judicial bench affect legal outcomes? Prior studies do not provide a clear answer, in part because they focus on how judges from different backgrounds---after controlling for other judicial characteristics---decide cases differently. In this article, we ask a simpler, but vital, question: do presidents' more diverse appointees, taken as they are, resolve cases differently than those presidents' other appointees? Using an original dataset of around 100,000 civil rights cases filed in 12 federal district courts, we find that the assignment of a case to a judge who is non-White or a woman has no statistically significant effect on case outcomes among Democratic appointees but causes more pro-defendant outcomes among Republican appointees. Our results are consistent with a theory of bargaining over judicial appointments in which Republican presidents take advantage of Democrats' concern over diversity on the bench to appoint more conservative judges.