DISPUTES that reach the Supreme Court tend to be hard cases—conflicts concerning government power or individual rights that confound and divide judges serving on lower courts. Hernández v Mesa, which revolves around the tragic death of a Mexican teenager on the Mexican border at the hands of an American border-patrol agent, is certainly such a case. After losing their district court hearing, the boy’s parents won their initial three-judge appeal at the Fifth Circuit Court of Appeals before losing again when the entire Fifth Circuit reconsidered the panel’s ruling. On February 21st, the Supreme Court went into the thicket.

Hernández’s topsy-turvy procedural path may seem surprising in light of the facts. In 2010, an unarmed 15-year-old, Sergio Hernández, was standing on Mexican soil when Jesus Mesa, an American border-patrol agent, killed him. Mr Mesa says the teenager had smuggled immigrants and, along with a few friends, was throwing rocks. But Mr Hernández’s parents insist—as video evidence appears to confirm—that he was just playing with friends. Running up the incline between the two countries (a concrete-paved “culvert” over the dried-up Rio Grande river) and daring to touch the American fence, one of Mr Hernández’s friends was grabbed by Mr Mesa before he could scamper down the incline. Sergio eluded capture, ran back down to the Mexican side and hid behind a pillar; but when he peeked out from his hiding spot, Mr Mesa fired and shot him in the face, killing him.

The boy’s parents would like to sue Mr Mesa for depriving their son of his fundamental right to life, a violation of the Fourth Amendment prohibition on unreasonable searches and seizures. Since the act took place on Mexican soil, Mr Mesa and the government counter, the constitution does not apply and the parents have no basis for a suit. As several of the Fifth Circuit judges wrote in their ruling, constitutional rights do “not protect all people in all places”. The on-off switch of constitutional protection implied by such a position may seem stark; the parents’ challenge, Justice Stephen Breyer said, is “very sympathetic”. But Robert Hilliard, the parents’ lawyer in his debut appearance before the justices, made the mistake of relying too heavily on the tragedy of it all. Mr Breyer and several of his colleagues, especially the conservative-leaning ones, seemed frustrated by Mr Hilliard’s inability to articulate a practical rule to govern not just Mr Mesa’s conduct but other extraterritorial rights claims that may come down the pike.

When pressed by Justice Elena Kagan to state “what exactly your rule is”, Mr Hilliard gave a rather self-serving answer that elicited a laughter-inspiring zinger from John Roberts, the chief justice. “Well”, he said, “that's a test that, surprisingly, fits the exact facts of your case”. Mr Roberts then asked Mr Hilliard how he would distinguish a cross-border shooting from “a drone strike in Iraq where the plane in piloted from Nevada”. If the parents can haul Mr Mesa to court for violating Mr Hernández’s constitutional rights, what’s to stop “anyone who suffers a drone strike” (Mr Breyer’s words) from coming “to New York and bring[ing] a law case”? Would the Supreme Court’s docket fill up with lawsuits brought by foreigners who had lost a leg or a family member in one of the 500-some drone strikes ordered during Barack Obama’s presidency, for example?

Mr Hilliard gave a string of unsatisfying answers to these questions, prompting Mr Breyer to remind him of a Supreme Court advocate’s role: “So what are the words that we write that enable you to win, which is what you want, and that avoid confusion, uncertainty, or decide these other cases the proper way? That's the question you've been given three times”, Mr Breyer told him, “and I would certainly like to know your answer.” After still more hemming and hawing through sceptical queries from Ms Kagan, Justices Anthony Kennedy and Samuel Alito, Mr Breyer’s exasperation reached a peak: it is one thing to say what the rule is, and quite another to explain why the court should adopt it. “[J]ust please”, he begged, “if there's anything else you have to say, I think you don't have anything else to say, but if you do, I would say this is a good time to say it”.

The liberal-leaning justices did their best to build the case Mr Hilliard could not when questioning Randolph Ortega and Edwin Kneedler, the two lawyers defending Mr Mesa’s position. Ms Kagan and Justice Ruth Bader Ginsburg teamed up with Mr Breyer to cast doubt on what Mr Ortega called the “very real and very finite” line of demarcation between Mexico and America. ”The dividing line isn't even marked on the ground”, Ms Kagan noted. “You can't tell on the ground where Mexico ends and the United States begins”. The space between the two countries is a “liminal area, which is kind of neither one thing nor another thing”. When the border area is fuzzy and jointly administered by two countries, Ms Ginsburg implied, there may indeed be good reason to hold border agents responsible for shooting teenaged pranksters in the face.

In the end, whether the boy’s parents will get a day in court to sue Mr Mesa may rest on the shoulders of Anthony Kennedy, so often the swing vote in contentious cases. Mr Kennedy asked difficult questions of both sides, betraying both sympathy with the parents and reticence to assert a profound judicial role “in one of the most sensitive areas of foreign affairs”; it may be better, he said, for the legislative and executive branches to “discuss with Mexico what the solution ought to be”. In view of the existing tensions between the Trump administration and the Mexican government over the question of a border wall, Mr Kennedy’s hope for reasoned rapport between the two parties may not be realistic. Nor does it provide any avenue for Mr Hernández’s parents to hold Mr Mesa accountable for killing their son.

A ruling in Hernández v Mesa may come by the end of June, but if the justices are split 4-4 (a vote that would leave the Fifth Circuit ruling in place without gilding it with precedential value), they could call for a new hearing once Neil Gorsuch, Mr Trump’s pick for the Supreme Court, takes his seat, as he is likely to do this spring. That would push the case into the new term beginning in October. It would give a full complement of justices a fresh chance to navigate a wrenching dilemma: encourage a flood of constitutional claims for piques suffered abroad or, perhaps, empower trigger-happy border-patrol agents to wield their authority—and their weapons—with impunity.