The government, in its petition asking the Supreme Court to hear the Slants case, Lee v. Tam, No. 15-1293, said that the trademark law did not ban any speech and that the Slants were free to continue to use their name.

All the law does, the brief said, is offer “federal benefits on terms that encourage private activity” in line with legislative policy.

In an unusual move, the band agreed that the justices should hear the government’s appeal, given the importance of the issues it presents. The band added that it should win on its First Amendment argument and two others: that the law is unconstitutionally vague and that “the Slants” is not disparaging.

The agency’s decisions are so inconsistent, the band’s brief said, that it “might as well be tossing a coin.” It has, for instance, rejected trademarks for “Heeb,” “Dago,” “Injun” and “Squaw,” saying they were disparaging. In other cases it has registered trademarks for those same terms.

In any event, the band said, it did not mean to disparage anyone. Its goal, it said, is to adopt and reform a disparaging term about Asians, much as some gay people have embraced the term “queer.”

The Redskins also maintain that they mean no offense. For many years, the trademark office agreed, registering Redskins trademarks in 1967, 1974, 1978 and 1990. In 2014, though, it reversed course and canceled six registrations, saying they disparaged Native Americans.

The team lost before a trial judge in Virginia and has appealed to the United States Court of Appeals for the Fourth Circuit, also in Virginia. The appeal is scheduled to be argued in December.