WASHINGTON — The Supreme Court on Thursday made it harder to strip citizenship from naturalized Americans. It also refused to grant new trials to defendants in a notorious 1984 Washington murder case and to a Massachusetts man whose lawyer failed to object to closing the courtroom for part of his trial.

Stripping Citizenship

The justices unanimously rejected the government’s position that it could revoke the citizenship of Americans who made even trivial misstatements in their naturalization proceedings.

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During arguments in April, several justices seemed indignant and incredulous at the government’s hard-line approach in the case, Maslenjak v. United States, No. 16-309.

They asked about a form that people seeking American citizenship must complete. It requires applicants to say, for instance, whether they had ever committed a criminal offense, however minor, even if there was no arrest. A government lawyer, in response to questioning, said that failing to disclose a speeding violation could be enough to revoke citizenship even years later.

Writing for the majority, Justice Elena Kagan said that the law required a tighter connection between the lie and the procurement of citizenship.

“We hold that the government must establish that an illegal act by the defendant played some role in her acquisition of citizenship,” she wrote. “When the illegal act is a false statement, that means demonstrating that the defendant lied about facts that would have mattered to an immigration official, because they would have justified denying naturalization or would predictably have led to other facts warranting that result.”

The case concerned Divna Maslenjak, an ethnic Serb who said she had faced persecution in Bosnia. She was granted refugee status, at least partly on that basis, and became a United States citizen in 2007.

In the process, she made a false statement about her husband, saying she and her family had also feared retribution because he had avoided conscription by the Bosnian Serb military. In fact, he had served in a Bosnian Serb military unit, one that had been implicated in war crimes.

When this came to light, Ms. Maslenjak was charged with obtaining her citizenship illegally. She sought to argue that her lie was immaterial, but the trial judge told the jury that any lie, however significant, was enough. Ms. Maslenjak was convicted, her citizenship was ordered revoked, and she and her husband were deported to Serbia.

The Supreme Court, having ruled that Ms. Maslenjak had been convicted under the wrong standard, returned the case to the lower courts to consider whether the government may try the case again under the stricter standard.

Given the significance of Ms. Maslenjak’s lie, she may lose again in a retrial.

Withheld Evidence

In a 6-to-2 decision in Turner v. United States, No. 15-1503, the court refused to grant new trials to seven defendants in a notorious 1984 murder in Washington, rejecting their arguments that prosecutors had withheld important evidence.

The defendants, almost all teenagers at the time, were prosecuted for sexually assaulting and killing Catherine Fuller, 48 at the time. Prosecutors presented no physical evidence, relying only on eyewitness testimony.

In 2010, 25 years after the trial, lawyers for the defendants sought to reopen the case, saying their convictions had been tainted by violations of Brady v. Maryland, a 1963 Supreme Court decision that required prosecutors to turn over favorable evidence to the defense. They said prosecutors had withheld several kinds of evidence, most notably about another suspect, James McMillan.

Justice Stephen G. Breyer, writing for the majority, said the withheld information would not have made a difference in the outcome of the trial.

“Considering the withheld evidence in the context of the entire record,” he wrote, “we conclude that it is too little, too weak or too distant from the main evidentiary points to meet Brady’s standards.”

Chief Justice John G. Roberts Jr. and Justices Anthony M. Kennedy, Clarence Thomas, Samuel A. Alito Jr. and Sonia Sotomayor joined the majority opinion. Justice Neil M. Gorsuch did not participate in the case, which was argued before he joined the court.

In dissent, Justice Kagan, joined by Justice Ruth Bader Ginsburg, wrote that the missing evidence would have changed the tenor of the trial, allowing the defendants to cast suspicion on Mr. McMillan rather than one another.

“The government got the case it most wanted — the one in which the defendants, each in an effort to save himself, formed something of a circular firing squad,” Justice Kagan wrote. “And the government avoided the case it most feared — the one in which the defendants acted jointly to show that a man known to assault women like Fuller committed her murder. The difference between the two cases lay in the government’s files — evidence of obvious relevance that prosecutors nonetheless chose to suppress.”

Closed Courtrooms

The court refused to grant a new trial to a Massachusetts man, Kentel Weaver, whose lawyer failed to object to the exclusion of the public from jury selection during his murder trial.

In 2010, the Supreme Court ruled that the Sixth Amendment guarantees criminal defendants the right to insist that jury selection be open to the public. The question in the new case, Weaver v. Massachusetts, No. 16-240, was whether a defendant was entitled to automatic reversal of his conviction in the context of a post-conviction challenge based on ineffective assistance of counsel.

Writing for the majority, Justice Kennedy said the answer was no.

“It is true that this case comes here on the assumption that the closure was a Sixth Amendment violation,” he wrote. “And it must be recognized that open trials ensure respect for the justice system and allow the press and the public to judge the proceedings that occur in our nation’s courts. Even so, the violation here did not pervade the whole trial or lead to basic unfairness.”

Justice Breyer, joined by Justice Kagan, dissented. He said that an error by a lawyer that led to a fundamental constitutional violation was enough to entitle a defendant to new trial, whether the error affected the result in the trial or not.