Lawyers for Richard Glossip and two other men on Oklahoma’s death row, who last month lost their challenge to their state’s controversial lethal injection protocol, have again asked the Supreme Court to consider their clients’ plight.

But the petition, filed Friday afternoon, does not ask the justices to reconsider their June 29 decision in Glossip v. Gross, which cleared the way for Oklahoma to use midazolam — a drug implicated in a number of botched executions — in its lethal injection protocol. Rather, the petition attacks the death penalty itself as a cruel and unusual punishment that violates the Eighth Amendment.

“It would be appropriate for the Court to use this case to address the constitutionality of the death penalty,” the pleading reads, “because the outcome will turn not on facts specific to any single litigant, but on circumstances common to the administration of the death penalty.”

The new petition, filed by federal public defenders, was written in direct response to a request by Justice Stephen Breyer, made as part of a 40-page dissent filed in Glossip, and joined by Justice Ruth Bader Ginsburg. Breyer’s dissent was a detailed, exhaustive attack on the death penalty’s many proven flaws, from its racial bias to the problems of error and misconduct. “[R]ather than try to patch up the death penalty’s legal wounds one at a time,” Breyer wrote, “I would ask for full briefing on a more basic question: whether the death penalty violates the Constitution.”

Today’s filing seeks to affirmatively answer that question, addressing several persistent pitfalls of the death penalty that were raised by Breyer and are embodied in the Oklahoma cases of three named plaintiffs — Richard Glossip, John Grant and Benjamin Cole. In particular, the petition picks up on Breyer’s criticism of the death penalty for its “lack of reliability, the arbitrary application of a serious and irreversible punishment [and the] individual suffering caused by long delays.”

In Glossip’s case, the petition directly addresses Breyer’s concern for the innocent people who have been sent to death row — and some potentially executed. Glossip has consistently maintained his innocence of the crime that sent him to die: the supposed murder-for-hire of his boss, Barry Van Treese, in 1997.

Indeed, The Intercept explored the case earlier this month, raising significant questions about his guilt. Glossip worked as a manager for a motel in Oklahoma City, which was owned by Van Treese. Nineteen-year-old Justin Sneed, who worked under Glossip, confessed to beating Van Treese to death — but then implicated Glossip, saying he had ordered Sneed to commit the murder. Sneed testified against Glossip to avoid a death sentence; he is serving life in a medium security prison. Aside from Sneed’s word, however, there was no evidence implicating Glossip in the crime. In fact, last fall, as Glossip faced an execution, Sneed’s daughter O’Ryan Justine Sneed wrote a letter to Oklahoma’s Pardon and Parole Board, asking the state to spare Glossip’s life. She said her father had lied to avoid the ultimate punishment and is now afraid to come forward, fearing the state would revoke his deal and sentence him to die.

The new petition before the Supreme Court argues that the courts are incapable of protecting an innocent person, such as Glossip, from being wrongly executed. But the Grant and Cole cases are deeply troubling as well — fraught with different problems that are endemic to the system as a whole.

Grant was sentenced to die for killing a kitchen worker while serving a 35-year prison sentence for robbery. According to the petition, his defense at trial was handled by “a lawyer who was new to the bar, who was self-medicating for untreated bipolar disorder, who married and then divorced her co-counsel in Mr. Grant’s case in less than one year — all during her representation of Mr. Grant — and who later voluntarily resigned from the bar after being suspended from practice.” The same attorney failed to present mitigating evidence that might have saved Grant from death row. “His sentence demonstrates the arbitrariness of capital sentencing,” the petition argues.

In the case of Cole, who confessed to brutally murdering his nine-month-old daughter in 2002, lawyers cite his untreated mental illness — he has been diagnosed as paranoid schizophrenic — as crippling to his attorneys’ attempts to represent him. On death row, Cole’s illness has worsened, exacerbated by years of extreme isolation. Oklahoma’s death row prisoners live in “underground housing with windowless cells and no access to open air or natural sunlight” and Cole “has not left his cell for years at a time.” These conditions, the petition argues, “also support rehearing and plenary consideration of the constitutionality of the death penalty.”

From his own underground cell — and as his September 16 execution date nears — Richard Glossip is encouraged by the decision of his lawyers to appeal. “It’s time to stand up and do this,” he told The Intercept on Thursday. “That’s what I want more than anything: stop the death penalty.” In his case, Glossip said, if the court does not do so, when he heads to the death chamber, the state of Oklahoma is “going to execute an innocent man.”