Two of the challenged broadcasts involved cursing on the Billboard Music Awards. The first involved Cher, who reflected on her career in accepting an award in 2002. “I’ve also had critics for the last 40 years saying I was on my way out every year,” she said.

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Then she, in the words of Justice Antonin Scalia in the earlier decision in the case, “metaphorically suggested a sexual act as a means of expressing hostility to her critics.” Justice Kennedy transcribed the crucial word as the letter F followed by three asterisks.

The second bout of celebrity cursing came in an exchange between Paris Hilton and Nicole Richie in 2003 in which Ms. Richie discussed in vulgar terms the difficulties in cleaning cow manure off a Prada purse.

The commission also took issue with a 2003 episode of “NYPD Blue” that included images of, in Justice Kennedy’s words, “the nude buttocks of an adult female character for approximately seven seconds and for a moment the side of her breast.”

In 2004, after the three broadcasts and in connection with cursing by the singer Bono at the Golden Globe Awards, the commission announced that broadcasts of even fleeting indecency were subject to punishment.

It did not matter, the commission said, that some of the offensive words did not refer directly to sexual or excretory functions. Nor did it matter that the cursing was isolated and apparently impromptu.

The commission imposed no punishment on Fox, but it fined ABC and its affiliates $1.24 million.

In the Fox case, the United States Court of Appeals for the Second Circuit, in New York, ruled that the commission was not entitled to change its policies “without providing a reasoned explanation justifying the about-face.” The Supreme Court reversed that ruling in 2009 on administrative-law grounds, returning it to the Second Circuit for consideration of the First Amendment issues.

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The appeals court then ruled that the commission’s policies were unconstitutionally vague. It later applied that reasoning to the ABC case.

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When the two cases made their way to the Supreme Court recently, one of them for a return trip, First Amendment advocates hoped for a square ruling from the justices on the constitutional issues. They were disappointed.

“This opinion leaves the commission free to modify its current indecency policy in light of its determination of the public interest and applicable legal requirements,” Justice Kennedy wrote. “And it leaves the courts free to review the current policy or any modified policy in light of its content and application.”

Justice Sonia Sotomayor, who was a judge on the Second Circuit before being appointed to the Supreme Court, recused herself from consideration of the F.C.C. case.

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Only Justice Ruth Bader Ginsburg, who voted with the majority but did not join its reasoning, was prepared to address the First Amendment issues raised by changes in the world of broadcasting and related media since 1978, when the Supreme Court decided the leading case in this area, Federal Communications Commission v. Pacifica.

That decision said the government could restrict George Carlin’s famous “seven dirty words” monologue, which had been broadcast on the radio in the afternoon. The court relied on what it called the uniquely pervasive nature of broadcast media and its unique accessibility to children.

Both points are open to question given the rise of cable television and the Internet.

“In my view,” Justice Ginsburg wrote, the Pacifica decision “was wrong when it issued. Time, technological advances, and the commission’s untenable rulings in the cases now before the court show why Pacifica bears reconsideration.”

In recent remarks before the American Constitution Society last week, Justice Ginsburg discussed the case, and she suggested wryly that there were gaps in the justices’ knowledge of popular culture.

“The Paris Hiltons of this world, my law clerks told me, eagerly await this decision,” she said of the case decided Thursday. “It is beyond my comprehension, I told my clerks, how the F.C.C. can claim jurisdiction to ban words spoken in a hotel on French soil.”