This article discusses the significance of two U.S. Supreme Court decisions considering, first, whether a court or arbitrator is to decide the threshold question of whether the Federal Arbitration Act’s statutory exclusion from arbitration of disputes involving “contracts of employment” is applicable to a contractual dispute, and second, whether a court or arbitrator should decide whether a motion to compel arbitration is “wholly groundless.” The results of the two cases, and their prospective significance, may surprise readers.