WASHINGTON — When the Supreme Court agreed to decide whether unhappy customers of DirecTV could band together in a class action, the court’s purpose seemed clear: to reverse and rebuke a California appeals court that had allowed the class action and refused to send the case to arbitration instead.

The Supreme Court is generally hostile to class actions and partial to arbitration, in which parties resolve disputes before private bodies. In 2011, in another case from California, it allowed companies to escape class actions by insisting on one-by-one arbitrations, even over trivial amounts of money, in standard-form contracts.

It was something of a surprise, then, that the case, argued on Tuesday, seemed to strike many of the justices as difficult. While there appeared to be a consensus that the appeals court had gone astray, there was also a sense that the Supreme Court had bitten off both less and more than it wanted to chew.

On the one hand, some justices questioned why they had volunteered to answer a trivial and idiosyncratic question about early termination fees. The arbitration agreement at issue has been abandoned by DirecTV and is not used by any other major company. Simply deciding the meaning of that defunct contract did not warrant the court’s attention, Justice Elena Kagan suggested.