Justices liberal and conservative indicated such a strategy - to concede guilt and plead for mercy to avoid execution - fell short of the constitutional guarantee of assistance of counsel. The justices did worry, though, about writing a broad opinion that could hobble an attorney's strategic decisions about how best to represent a client.
The court was considering the actions of Larry English, at the time a lawyer in Louisiana. English told a jury that, despite his client Robert L. McCoy's repeated claim of innocence, McCoy had killed three family members. The hope was that the concession would win trust from the jurors and lead them to spare McCoy from the death penalty.
The strategy was unsuccessful, and McCoy contends he deserves a new trial.
"I totally understand that this lawyer was in a terrible position because this lawyer wants to defeat the death penalty," Justice Elena Kagan told Louisiana Solicitor General Elizabeth Murrill. "And he has a client who says: That's not my goal here."
Kagan continued: "But the question is, when that happens, does the lawyer have to step back and say: You know what? That's not his goal. His goal is to avoid admitting that he killed his family members."
Justice Neal M. Gorsuch followed: "Can we even call it assistance of counsel? Is that what it is when a lawyer overrides that person's wishes?"
Murrill said it would have been a "futile charade" for English to try to convince a jury of McCoy's innocence.
He was convicted of killing his estranged wife's mother, stepfather and son in 2008 after she had left him and gone into protective custody. Each of the victims was shot at close range.
In a 911 call, McCoy's mother-in-law, Christine Colston Young, could be heard screaming: "She ain't here, Robert! I don't know where she is! The detectives have her!" A gunshot was then heard on the 911 tape, and the call was disconnected.
A car later found to be McCoy's was seen leaving the area, and police officers discovered in the abandoned vehicle the phone that Young had used. McCoy was arrested in Idaho after hitchhiking rides from truckers. The gun used in the killings was found with him. In custody, McCoy tried to hang himself.
But he maintained his innocence, alleging a conspiracy among local police officers to commit the murders and frame him. His first public defender was let go because of differences between attorney and client, and then McCoy's parents paid English $5,000 to represent their son.
"How does the lawyer back up that defense - 'I didn't do it' - when, in the lawyer's view, there is no basis for taking that position?" Justice Ruth Bader Ginsburg asked.
Seth Waxman, McCoy's attorney at the Supreme Court, said a lawyer does not have to aid a client lying on the stand but does have an obligation to make the state prove its case, and to strenuously cross-examine the state's witnesses.
Many of the justices' questions were not about McCoy's case but about how to draw lines in cases perhaps not as extreme.
Chief Justice John Roberts and Justice Samuel Alito pressed Waxman on whether a lawyer could concede any element of a crime - crossing a state line, for instance, if there were irrefutable evidence that had occurred. Waxman said no.
"If there is a contemporaneous objection, the trial court may not permit the defense lawyer to admit any element of the offense," Waxman said.
Justice Stephen Breyer said rules that would prevent lawyers from making strategic decisions worried him.
"A large percentage of the people that insist on representing themselves, particularly in death cases, are going to walk right into the death chamber," Breyer said. "A lot of the people there are just not really capable of managing their own defense."
But the harder questions were for Murrill.
"Can I take away from your argument that the state of Louisiana says that if a defendant wants to plead not guilty, the defense attorney can plead guilty if the defense attorney thinks that's the best way to avoid the death penalty?" Justice Anthony Kennedy asked.
Murrill said no, because the prosecution in McCoy's case still had to prove his guilt.
But other justices said that was much easier when English told the jury that McCoy had killed the three victims.
The case is McCoy v. Louisiana.