The Supreme Court agreed today to decide the constitutionality of a 50-year-old Virginia law that prohibits burning a cross ''with the intent of intimidating any person or group of persons.''

The case is an appeal by the state from a decision of the Virginia Supreme Court, which held in a 4-to-3 ruling last November that burning a cross, no less than burning an American flag, was symbolic speech protected by the First Amendment.

The state court decision grew out of two prosecutions in 1998, one of two white men who burned a cross in the yard of a black neighbor in Virginia Beach, and one of a Ku Klux Klan leader in rural Carroll County, who presided over a rally and the burning of a 30-foot cross that was visible for three-quarters of a mile along a state highway.

In hearing the state's appeal, the justices will revisit a subject they last confronted 10 years ago, when the court overturned a cross-burning ordinance in St. Paul, in a 5-to-4 decision that fell well short of resolving a societywide debate over the relationship between free speech and hate speech.

Thirteen states and the District of Columbia have criminal prohibitions against cross burning, and the state and lower federal courts have continued to issue conflicting rulings since the Supreme Court's 1992 decision in R.A.V. v. City of St. Paul.

The attorneys general of Arizona, California, Georgia, Kansas, Massachusetts, Missouri, Oklahoma, Utah and Washington all signed a brief urging the justices to hear Virginia's appeal. ''Cross burning is an especially virulent, even unique, form of intimidation in American society'' that states should be able to prohibit, the brief said.

One reason for the continuing confusion is a disagreement among judges and legal scholars over how to interpret the Supreme Court's last decision. The St. Paul ordinance that the court invalidated made it a crime to place a symbol, including a burning cross, ''which one knows or has reasonable grounds to know arouses anger, alarm or resentment in others on the basis of race, color, creed, religion or gender.''

According to the court's majority opinion, written by Justice Antonin Scalia, this description of the prohibited conduct amounted to ''content-based discrimination'' because it ruled symbolic speech in or out depending on the groups that the speech targeted.

The Virginia law, which was enacted in response to highly publicized Ku Klux Klan cross burnings in the late 1940's and early 1950's, does not refer to any particular group. The law provides that ''it shall be unlawful for any person or persons, with the intent of intimidating any person or group of persons, to burn, or cause to be burned, a cross on the property of another, a highway or other public place.''

In finding the law unconstitutional, the Virginia Supreme Court's majority said that despite the lack of reference to any specific target, the law was nonetheless ''analytically indistinguishable'' from the St. Paul ordinance. The Virginia law was in its own way just as selective, the state court said, because it proscribed not all intimidating expression but ''selectively chooses only cross burning because of its distinctive message.''

Virginia's attorney general, Jerry W. Kilgore, said in the state's appeal, Virginia v. Black, No. 01-1107, that the law's sole focus on cross burning was justified by the sense of threat associated with the practice. Even a ''white, middle-class Protestant waking up at night to find a burning cross'' outside his home would feel more threatened than if he found ''say, a burning circle or square,'' Mr. Kilgore's brief said, adding: ''In the latter case, he may call the fire department. In the former, he will probably call the police.''

The three defendants, Barry E. Black, Richard J. Elliott and Jonathan O'Mara, are represented by a well-known First Amendment scholar, Rodney A. Smolla of the T.C. Williams School of Law at the University of Richmond, and by the American Civil Liberties Union of Virginia and private lawyers. Urging the justices to reject the appeal, they said the Virginia Supreme Court ''conscientiously applied core First Amendment principles in unpalatable circumstances.''

There were these other developments at the court today:

Effective Counsel

Voting 8 to 1, the court overturned a federal appeals court's ruling that set aside the death sentence of a Tennessee man convicted of a double murder. The United States Court of Appeals for the Sixth Circuit, in Cincinnati, had granted Gary B. Cone's petition for a writ of habeas corpus on the ground that his lawyer's handling of the sentencing hearing was so deficient as to have violated the Sixth Amendment right to the effective assistance of counsel.

The lawyer, in whom mental illness was diagnosed and who later committed suicide, failed to present mitigating evidence to the jury and did not make a closing argument.

Writing for the court today, Chief Justice William H. Rehnquist said that under the circumstances, forgoing a closing argument could be seen as ''a tactical decision about which competent lawyers might disagree'' because it deprived the state's highly effective lead prosecutor of the chance to make a rebuttal argument in the moments before the jury retired for its deliberations.

Consequently, Chief Justice Rehnquist said, it was not unreasonable for Tennessee's appellate court to find no constitutional violation in the lawyer's performance.

The decision, Bell v. Cone, No. 01-400, was the latest of the Supreme Court's efforts to apply a 1996 federal law, Anti-Terrorism and Effective Death Penalty Act, which significantly circumscribed the jurisdiction of federal courts to review state court decisions through habeas corpus petitions.

Under the law, federal courts may not grant petitions unless the state court proceedings ''resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established federal law'' as defined by the Supreme Court's precedents.

The dispute in this case centered on which of two competing Supreme Court precedents on the effective assistance of counsel, issued on the same day in 1984, properly applied to the circumstances of Mr. Cone's sentencing. The Sixth Circuit applied one precedent, United States v. Cronic, which is favorable to defendants and creates a presumption that a lawyer who ''entirely fails to subject the prosecution's case to meaningful adversarial testing'' has been ineffective. In a dissenting opinion today, Justice John Paul Stevens argued that the appeals court had properly applied the Cronic precedent to rule in Mr. Cone's favor.

But the majority said the Tennessee appeals court had been correct to apply the other precedent, Strickland v. Washington, which is much less favorable to defendants and requires proof not only that a lawyer's performance ''fell below an objective standard of reasonableness'' but also that the outcome would otherwise have been different.

While considering the Cone case, the justices have deferred action in a death penalty case from Texas that raises a similar analytical issue. In this case, Cockrell v. Burdine, No. 01-495, the United States Court of Appeals for the Fifth Circuit overturned the death sentence for a man, Calvin J. Burdine, whose lawyer slept through parts of his trial. The Fifth Circuit, in New Orleans, held that ineffectiveness should be presumed under the Cronic precedent. The justices are likely to act shortly on the appeal filed by the Texas attorney general, John Cornyn.

Conspiracy Law

The court accepted an appeal from the federal government and agreed to decide an important question of the law of criminal conspiracies: whether a conspiracy should be deemed to have ended when the government frustrates its objective. As in this case, United States v. Recio, No. 01-1184, the question typically arises when the government has intercepted a shipment of drugs and has arrested the courier, unbeknown to the other members of the conspiracy, who continue with their activities even though they can no longer accomplish their goal.

The United States Court of Appeals for the Ninth Circuit, applying a doctrine it developed in the late 1990's that a conspiracy must be deemed to have terminated when its objectives have become impossible, overturned a drug conspiracy conviction of two men who arrived at an Idaho shopping mall to claim a drug shipment that the government had already intercepted.

In its Supreme Court appeal, the government argued that the Ninth Circuit's approach, with which other appeals courts disagree, would discourage ''legitimate law enforcement methods that can be of vital importance not only in drug cases, but also in violent crime, terrorism and other contexts in which prosecution of the conspirators and frustration of their goals are both crucial objectives.''

Photo: Jonathan O'Mara, one of three defendants in a Virginia Beach cross-burning case. (Associated Press)