When Uber demanded this week that Google submit its driverless-car trade secret claims to arbitration, the idea seemed like a head-scratcher. What grounds would Uber have to force Google subsidiary Waymo LLC to give up its right to a jury trial?

But Uber’s initial motion to compel arbitration was heavily redacted—at Waymo’s insistence, according to Uber. Under pressure from U.S. District Judge William Alsup, the parties agreed to remove all the redactions Thursday.