The Supreme Court in recent years has made efforts to change the demographic composition of juries. These effects are in part explainable on the basis of fairness to prospective jurors; but the Court also suggests that the demographic composition of the jury is important to the fairness of the trial. In some respects fairness may be improved by a jury demographically close to the defendant, while in other respects it may be improved by a diverse jury or a jury representative of the community. These effects occur only if there are real differences among demographic groups; however, the existence of such differences precludes the simultaneous achievement of both types of effects. Further, random selection of jurors prevents the optimization of either set of effects. I conclude that recent changes in jury selection law do not improve the fairness of the trial process, but only the appearance of fairness.