The Supreme Court on Tuesday turned down a Louisiana murderer’s request that the justices take his case to decide whether the death penalty is unconstitutional.

Lamondre Tucker drew noted support only from the two justices who previously have said the court should consider the question: Stephen G. Breyer and Ruth Bader Ginsburg.

Last term, Breyer wrote a lengthy dissent in a case upholding a lethal-injection technique to say that the court should once again take a broader look at the issue of the death penalty. He said he believed that for a number of reasons the current death-penalty system violates the Constitution.

“In 1976, the court thought that the constitutional infirmities in the death penalty could be healed; the court in effect delegated significant responsibility to the States to develop procedures that would protect against those constitutional problems,” Breyer wrote. “Almost 40 years of studies, surveys, and experience strongly indicate, however, that this effort has failed.”

Some death-penalty opponents think Breyer was signaling that a majority on the court might be willing to take up the question.

But Tucker’s attorney, G. Ben Cohen, said that the death of Justice Antonin Scalia in February may have hurt his client’s chances, “which is something I never thought I’d say.”

Scalia was adamant that the Constitution allows capital punishment. But Cohen, who works for the Promise of Justice Initiative in New Orleans, said it did not seem likely that an ideologically divided court would take up such a controversial case.

“I think the court is less likely to [accept] an issue like capital punishment with only eight members,” Cohen said.

Breyer said last term that the “imposition and implementation of the death penalty seems capricious, random, indeed, arbitrary,” and in Tuesday’s dissent he said Tucker’s case fit that bill.

Tucker, who has a low IQ, was just 18 in 2008 when he murdered his pregnant girlfriend. The court in recent years has ruled that neither juveniles nor the intellectually disabled are eligible for execution.

Moreover, Breyer wrote, Tucker was convicted and sentenced to death in Caddo Parish, which “imposes almost half the death sentences in Louisiana, even though it accounts for only 5 percent of the state’s population and 5 percent of its homicides.” Breyer wrote.

“Given these facts, Tucker may well have received the death penalty not because of the comparative egregiousness of his crime, but because of an arbitrary feature of his case, namely, geography,” Breyer wrote.

“One could reasonably believe that if Tucker had committed the same crime but been tried and sentenced just across the Red River in, say, Bossier Parish, he would not now be on death row,” he wrote.

Death-penalty opponents had been divided about when would be the best time to bring a case that directly challenged the constitutionality of the death penalty. But Cohen said lawyers have no choice but to act when they believe their clients’ lives are at stake.

Still, even though it turned down the challenge in Tucker v. Louisiana, the court continues to refine the sentencing process in capital-punishment cases. Also on Tuesday the court issued an unsigned opinion siding with Shawn Patrick Lynch, who was sentenced to death in Arizona for murdering a man that he and a friend met in a bar.

Prosecutors had argued Lynch deserved death because he posed a risk to others in the future. But defense lawyers were kept from telling the jury that the alternative sentence was life in prison without the possibility of parole.

The Arizona Supreme Court upheld the sentence, but the U.S. Supreme Court said the jury must be told about the alternative sentence.

Justices Clarence Thomas and Samuel A. Alito Jr. protested the “remarkably aggressive use of our power to review the states’ highest courts.” Thomas said the court was imposing a “magic-words requirement” into jury instructions.

The case is Lynch v. Arizona.