The Supreme Court announced yesterday that it would once again consider whether to overrule two recent decisions and allow juries in death penalty cases to hear testimony about the character of the victim and the impact of the murder on the victim's survivors.

The justices yesterday specifically asked both sides in a Tennessee murder case to address the issue of whether the court should overrule the 1987 decision in Booth v. Maryland, which disallowed such evidence. A majority of the court is on record as disagreeing with Booth and many observers believe the justices are prepared to jettison it and a related 1989 decision that the court also said it would consider overruling.

Yesterday's order was issued less than a month after it dismissed, apparently because of technical legal problems, an Ohio case in which the state had asked that Booth be overruled. It seemed to suggest that justices opposed to Booth were eager to find another opportunity to consider doing away with it.

It also took the form of a highly unusual Friday afternoon order -- a departure from the court's usual schedule for announcing which cases it will review -- in which the justices ordered briefs to be filed on a speedy schedule so that the case could be argued in April and decided by July.

Three justices dissented from the action. Justice John Paul Stevens, in a one-paragraph dissent joined by Thurgood Marshall and Harry A. Blackmun, said the move to put the case on a fast track and expand it to include consideration of whether to overrule Booth "is both unwise and unnecessary."

The case, Payne v. Tennessee, concerns Pervis Payne, a borderline retarded black man, 20, with no previous criminal record, who was convicted of stabbing to death Charisse Christopher, 28, a white woman, and her 2-year-old daughter, and intending to murder her 3-year-old son.

At the sentencing part of the trial, the prosecution presented testimony from the mother and grandmother of the victims, who described the devastating effect of the murders on the surviving child. "He cries for his mother," one witness, Mary Zvolanek, said of her grandson Nicholas. "He doesn't seem to understand why she doesn't come home. And he cries for his sister, Lacie."

The prosecution also introduced a grisly color videotape of the crime scene, including a wide-angle shot of mother and daughter lying in a pool of blood, and close-ups of their bodies.

"There obviously is nothing you can do for Charisse or Lacie," the prosecutor told the jury. "But there is something you can do for Nicholas."

He then approached a large diagram of Nicholas Christopher's body and stabbed through it with the butcher knife found at the crime scene.

The Tennessee Supreme Court upheld the conviction and death sentence. In asking the Supreme Court to review that ruling, Payne's lawyers argued that the videotape was so inflammatory that it should not have been allowed into evidence. They said Zvolanek's testimony and the prosecutor's statements about the impact of the crime were "clearly condemn{ed}" by the holdings of Booth and the 1989 case, South Carolina v. Gathers.

Lawyers for the state, which asked the court not to hear the case, said the testimony was relevant because "part of what makes the crime in this case so heinous and cruel . . . is that it involved the murder of Nicholas's mother and sister."