At the end of this month, the Supreme Court will reckon with execution by lethal injection in Glossip v. Gross, the case of Oklahoma death-row inmates who are challenging the three-drug protocol that the state has chosen to carry out death sentences.

In the history of capital punishment in America, the 2010 case of Jeffrey Landrigan seems inconsequential, but it is worth revisiting now because it shows how hard the conservative majority has tried to avoid grappling with the grisly realities of this execution method and, really, with the death penalty in general. It also helps to explain why the national system for administering capital punishment is in such turmoil, with executions now halted because of concerns about lethal injection in fifteen of the thirty-two states where the death sentence is still an option.

Arizona convicted Landrigan of murder and scheduled his execution, but a shortage in the United States of the barbiturate called sodium thiopental threw off that plan. Almost all states with the death penalty were then using three drugs for executions—a short-acting anesthetic followed by a paralyzing agent and then a heart-stopping drug. Sodium thiopental was meant to be the anesthetic. From a foreign wholesaler, later identified as Dream Pharma, a fly-by-night business run out of a driving school in London, the state of Arizona bought some made by a German company in Austria. It was allowed into the United States in violation of federal law, and it was neither checked nor approved by the Food and Drug Administration.

In federal court, Landrigan’s lawyers asked the state to confirm its effectiveness, so he wouldn’t suffer the agony that the other drugs were known to cause if the anesthetic didn’t work. The state refused the request to provide that proof. The trial judge ordered it to do so, and Arizona defied the order. The judge stayed the execution. Without F.D.A. approval or proof from the state, she wrote, she couldn’t determine whether the drug would actually anesthetize Landrigan.

The state’s secretiveness especially “perplexed” her. She wrote that she had “never experienced a situation such as this where a defendant opposes a motion for emergency relief by claiming it has the evidence necessary for resolution of the matter but that evidence should not be produced.” The U.S. Court of Appeals for the Ninth Circuit affirmed her ruling.

But then the Supreme Court’s five conservatives, in an order written by Justice Anthony Kennedy over the dissenting votes of the four moderate liberals, quickly vacated the stay. “There is no evidence in the record to suggest that the drug obtained from a foreign source is unsafe,” Kennedy wrote. Arizona executed Landrigan that night.

Kennedy disregarded what the trial and appeals courts had found about the increased risk from a drug provided by a source the F.D.A. didn’t approve, which was evidence in the record. He also ignored the central reason for the stay of execution: that Arizona had defied an order from a federal judge to produce evidence that the sodium thiopental obtained for the execution would be effective as an anesthetic.

A few months later, the Justice Department told Arizona that it could not use any more of the drug from the batch used to kill Landrigan because the state had obtained it illegally. In 2012, a federal district judge in Washington, D.C., confirmed that the drug was illegally imported and ordered the F.D.A. to immediately obtain whatever remained from Arizona and other states that bought the drug from Dream Pharma.

The debate over lethal injection dates back to 1976, when the Supreme Court reinstated capital punishment after a ten-year moratorium. The following year, as Jeffrey Toobin explained, Oklahoma chose it as a supposedly humane alternative to the then-preferred, clearly excruciating methods of execution—strapping a convict to a chair and pulsing electricity through his body until he died of shock or choking him to death by making him breathe poisonous gas in a sealed chamber.

In making the choice, the Oklahoma legislature consulted no experts and did no studies on the procedure before adopting it as the state’s primary method of execution. The legislature left to prison officials, not trained for this task, decisions about which drugs to use, how much of each, and how to administer them.

None of the many other states that later adopted lethal injection as their method of execution made up for the slapdash way that Oklahoma developed the procedure by doing studies of their own. In 2008, Alison J. Nathan, who was then a law professor and is now a federal trial judge in New York City, wrote, “Historical accident (or what sociologists would call a ‘cascade to mistaken consensus’) explains far better than science or medicine the current ubiquity of the three-drug protocol.”

There have been more than fourteen hundred executions in the United States since the Supreme Court reinstated the death penalty, almost nine out of every ten by lethal injection. There have been dozens of accounts of ghastly executions by lethal injection gone wrong, especially since 2011, when sodium thiopental became unobtainable. As states have experimented with new drug combinations, they have introduced new uncertainties about the effects of lethal injection. Nine states have used or plan to use drugs from compounding pharmacies, whose products are not approved by the F.D.A.

One experiment the Court could not ignore was carried out a year ago on Clayton D. Lockett in Oklahoma, a case that Paige Williams described in The New Yorker. The executioner tried and failed at least twelve times to find a usable vein for delivering the injections. After almost an hour, he found one in Lockett’s groin. Seven minutes after he was given a sedative, Lockett was deemed ready and the lethal drugs were administered. Then, “after being declared unconscious,” lawyers for the death-row inmates told the Court, “he began to speak, buck, raise his head, and writhe against the gurney.” A federal appeals court reported, “In particular, witnesses heard Lockett say: ‘This shit is fucking with my mind,’ ‘Something is wrong,’ and ‘The drugs aren’t working.’ ” About twenty minutes later, when the state’s director of corrections thought that Lockett had not received enough of the execution drugs to kill him and that there was not enough of them left to complete the execution, he ordered the executioner to stop administering any drugs. Lockett died anyway soon after.

In executing Lockett, Oklahoma used for the first time as the anesthetic a sedative called midazolam, which is usually employed to treat serious seizures and severe insomnia. As lawyers for the inmates told the Court, it has no pain-relieving properties, hasn’t been approved by the F.D.A. to maintain general anesthesia in surgical operations, and has a “ceiling effect,” meaning that even a large dose of it may not put someone under. The lawyers noted that “there are actual scientific and medical data demonstrating that midazolam cannot reliably render a person unconscious and insensate for purposes of undergoing surgery.”

Nevertheless, Arizona, Florida, and Ohio used midazolam in executions last year. In Arizona and Ohio, the deaths of the inmates were so protracted and painful that the states began looking for alternative drugs to use instead. In February, the Florida Supreme Court ordered the state government not to execute an inmate by the same combination of drugs used on Lockett until the U.S. Supreme Court resolves the issue. Roche and Akorn, which make midazolam, have declared their opposition to its use in executions.