The Supreme Court said yesterday that criminals appealing their convictions have a right to "effective" assistance from their lawyers.

The court, in a 7-to-2 decision written by Justice William J. Brennan, extended a 1963 ruling that indigent defendants have a right to have a lawyer handle a first appeal of their convictions.

The right to a lawyer would be a "futile gesture" unless it included a right to have effective assistance, Brennan wrote in the case of a drug dealer from Kentucky. The man's lawyer failed to comply with all the requirements of Kentucky's court procedures, and the appeal was thrown out.

Brennan said that when states give criminals the right to appeal, the lawyers involved, whether paid by the state or by the criminal, must provide effective help, he said.

Justice William H. Rehnquist, joined by Chief Justice Warren E. Burger, dissented, saying that the decision would give convicts another means to tie up the courts with frivolous appeals. The case is Evitts v. Lucey.

In another criminal case, the high court made it easier yesterday for prosecutors to keep people who object to capital punishment from sitting on juries in cases where the death penalty might be imposed.

A federal appeals court in Atlanta in 1983 threw out the death sentence of a child murderer, saying that a prospective juror who indicated having reservations about the death penalty was improperly excluded.

Rehnquist, writing for a seven-member majority, reinstated the death sentence. Rehnquist said state trial judges have broad discretion in deciding who can sit on juries in potential capital punishment cases.

The court in 1968 said jurors opposed to capital punishment could be excused only if their opposition would make it impossible to be impartial. Rehnquist yesterday said that a judge can act even if a juror's bias has not been shown with "unmistakable clarity."

Brennan, joined by Justice Thurgood Marshall, dissented, calling the ruling in Wainwright v. Witt an "unexplained evisceration" of the protections given defendants in the 1968 case.

Brennan said the court majority "increasingly acts as the adjunct . . . of the prosecutors in facilitating efficient and expedient conviction and execution . . . despite the Constitution's fundamental guarantee. One can only hope that this day, too, will soon pass."

In another criminal case, the court broadened police powers to search for drugs without warrants. The court, in an opinion by Justice Sandra Day O'Connor, ruled 7 to 2 that law enforcement officials acted properly in conducting a warrantless search of a pickup truck even though they waited until three days after they seized the truck. Brennan and Marshall dissented in U.S. v. Johns.

In a fourth decision, the court ruled 8 to 1 that a city can be held liable for damages assessed against a top city official if he is sued "in his official capacity."

Justice John Paul Stevens, writing for the majority in Brandon v. Holt, said the city of Memphis, Tenn., may have to pay damages to a couple injured by an allegedly unstable police officer because the couple's lawsuit in effect was against the city, even if it named only the chief of police as a defendant. Rehnquist dissented.

In other action yesterday, the court also agreed to hear the case of a suspected drug courier from Colombia who was held for 16 hours before U.S. Customs officers at Los Angeles International Airport obtained a court order to examine her abdominal cavity.

The woman aroused suspicion because she fit a "profile" of drug smugglers -- she often came to this country for short visits, had no luggage and no place to stay. Customs officials found no drugs when they strip-searched her, but she refused to consent to an X-ray search of her abdomen.

Customs officials detained her and refused to allow her to go to the bathroom unmonitored. She in turn refused food and water. Agents finally secured a court order for a body cavity search. The examination revealed one balloon of cocaine. Over the next four days she excreted an additional 87 balloons of cocaine totaling more than one pound of the drug.

The case is U.S. v. De Hernandez.