The clock is ticking again on executions in California.

The state Supreme Court’s ruling Thursday, upholding much of a prosecution-backed initiative seeking to speed up the death penalty process, cleared the way for the prison system to approve new rules for lethal injections for the first time in more than a decade. If a federal judge finds the procedures constitutional, execution dates could be set within a year for 18 prisoners, including four from the Bay Area, whose final appeals of their death sentences have been rejected.

California, which has nearly 750 inmates on the nation’s largest Death Row, last performed an execution in January 2006. Shortly afterward, U.S. District Judge Jeremy Fogel of San Jose halted further executions until the state fixed problems in injection procedures and staff training that, he said, created a serious risk of a botched and agonizing execution in violation of constitutional standards.

Fogel later left the bench to run the Federal Judicial Center and the case was reassigned to U.S. District Judge Richard Seeborg of San Francisco, who has stayed all pending executions. Meanwhile, state prison officials rewrote the injection procedures, were rejected by a state judge for failing to hold public hearings, and were then sued by murder victims’ families for allegedly dragging their feet on the regulations.

Gov. Jerry Brown’s administration settled the suit and agreed to draft new procedures for executions with a single lethal barbiturate, replacing the now-unavailable three-drug combination the state had used since 1996. The rules drew thousands of public comments, mostly critical — but officials now can disregard those objections and make the procedures final under a provision of Proposition 66, the November ballot measure that the state’s high court upheld Thursday.

When prosecutors seek their first new execution date, Seeborg will decide whether the new procedures contain adequate safeguards, considering defense lawyers’ objections that the drugs on California’s approved list are untested in executions.

But Kent Scheidegger, legal director of the Criminal Justice Legal Foundation and an author of Prop. 66, noted that the U.S. Supreme Court, whose rulings Seeborg must follow, has given states considerable leeway in execution procedures. In 2015, the court allowed Oklahoma to use a drug that had appeared to cause prolonged suffering at a previous execution, with Justice Samuel Alito saying it was up to inmates to propose a less-painful method.

Here is a look at the cases of the Bay Area inmates who are now in Seeborg’s court:

•Anthony “Jack” Sully, a former Millbrae police officer, was convicted of six murders related to drugs and prostitution during a six-month period in 1983, while he was running an electrical contracting business in a Burlingame warehouse.

A federal appeals court said that Sully, while addicted to cocaine, invested in an “escort service” that employed prostitutes and that he brutally murdered some of the women. Four of his victims were prostitutes, another was a man who may have been a pimp, and the sixth was a woman who offered to sell Sully cocaine, the court said. Sully denied committing the murders, and his lawyer argued, unsuccessfully, that Sully’s trial attorney failed to investigate evidence that Sully was mentally ill.

•Robert Fairbank pleaded guilty to torturing and murdering a San Francisco State University student, Wendy Cheek, 24, whose charred body was found in December 1985 near a reservoir in San Mateo.

Four days before the murder, a San Francisco judge had released Fairbank without bail after his arrest on a rape charge.

The federal appeals court that upheld his death sentence rejected a defense claim that Fairbank’s trial lawyer had represented him incompetently by not looking into evidence of possible brain damage and by making critical comments about him to the jury.

•David Raley was a security guard in 1985 when he took two teenage girls on a tour of a deserted Hillsborough mansion, then raped and stabbed them, tied them up and threw them down a ravine, killing one of them, 16-year-old Jeanine Grinsell of San Mateo.

The jury that convicted him of murder deadlocked 7-5 in favor of a death sentence, but prosecutors won a unanimous death verdict from a new jury at a penalty retrial. The appeals court rejected a defense argument that Raley’s lawyers should have presented psychiatric testimony and noted that jurors had heard evidence about physical and emotional abuse by Raley’s alcoholic mother.

•Harvey Heishman of San Leandro was convicted of the 1979 murder of an Oakland woman who was about to testify that he had sexually assaulted her. Heishman, a previously convicted rapist, had been arrested after Nancy Lugassy, 28, told police he had raped her, and then released on bail. She was planning to testify against him at an upcoming hearing when she was shot to death in her front yard.

One witness who said she was involved in Heishman’s murder plot was exposed as a congenital liar during courtroom questioning, but the appeals court found adequate evidence to support the jury’s guilty verdict. The court also rejected defense arguments that Heishman’s trial lawyers failed to look fully into the abuse he had suffered as a child.

Bob Egelko is a San Francisco Chronicle staff writer. Email: begelko@sfchronicle.com Twitter: @egelko