For as long as America has had the death penalty, there have been questions about how best to carry it out. The execution of Kenneth Eugene Smith in Alabama on Thursday, the first American execution in which death was caused by suffocation with nitrogen gas, gave no indication of settling the legal, moral and technical questions that have long bedeviled states as they mete out the ultimate punishment.

Most recently, problems with the purchasing, administration and effects of lethal injection drugs have sent states scrambling for alternatives ranging from the old — firing squads, electric chairs and gas chambers — to the untested, like Alabama’s use of a mask to force Mr. Smith to inhale nitrogen instead of air.

But after Mr. Smith’s death, the Alabama attorney general, Steve Marshall, hailed the execution as a “historic” breakthrough. He criticized opponents of the death penalty for pressuring “anyone assisting states in the process.”

“They don’t care that Alabama’s new method is humane and effective, because they know it is also easy to carry out,” he said in a statement.

Beginning in 2015, Oklahoma, Mississippi and then Alabama became the first three states to authorize the use of nitrogen hypoxia in executions. Oklahoma and Mississippi specified it as a backup method if lethal injections were ruled unconstitutional or if the drugs used in them became unavailable. Alabama offered death-row inmates a choice between nitrogen hypoxia and lethal injection.

Mr. Smith chose nitrogen after he survived an hourslong attempt to execute him by lethal injection in 2022, during which he was repeatedly stabbed with needles and placed in what he called an “inverted crucifixion position.” But he continued to wage a legal battle against the use of the method and the state’s protocol for administering it.

Even states that have considered the use of less common methods of capital punishment have been hesitant to use them. In 2021, the South Carolina legislature authorized execution by electric chair or firing squad but then passed a law shielding the identities of drug companies and officials involved in executions from public view, making it easier to obtain the needed drugs. The state then announced that it was prepared to resume lethal injections.

In 2018, the director of the Oklahoma prison system announced that the state would start using nitrogen gas, complaining that he had spent his time in office on a “mad hunt” for lethal injection drugs that involved having to converse with “seedy individuals” and make calls to the “back streets of the Indian subcontinent.”

But the change never happened. In 2020, the state said it too had obtained the necessary drugs to perform lethal injections. Critics said the three states had authorized the use of nitrogen without adopting a protocol for actually using it. Alabama is the only state to eventually have developed one.

At least one other state, Nebraska, is considering a bill that would authorize the use of nitrogen hypoxia. Nebraska last executed a prisoner in 2018, its stockpile of lethal injection drugs has expired, and it has no way to execute the 11 people on its death row, according to The Lincoln Journal Star.

In general, states prefer to tinker with their existing execution protocols rather than try something new, said Deborah Denno, a professor at Fordham University Law School. “States will stick to the same method as long as they possibly can, because if they change, they’re conceding that there’s been a problem,” she said.

She said it was difficult to predict whether the apparently successful execution of Mr. Smith would make other states more apt to consider adopting nitrogen hypoxia. The number of executions has dwindled over time from a high of 98 in 1999 to a low of 11 in 2021.

The decrease has a variety of causes, including restrictions on executing the cognitively disabled, increased awareness of wrongful convictions and racial disparities, and restrictions by pharmaceutical companies on the use of their products.

The numbers have begun to inch up again as states have found ways to acquire lethal injection drugs or have come up with new protocols.

Such adjustments have happened before. When hangings were considered slow and grisly, and an unseemly form of public entertainment, executioners tried to improve things by using gallows instead of tree limbs, and then scaffolds instead of gallows, Ms. Denno has written. But the efforts were “plagued by guesswork and inconsistency,” she said.

Eventually, a New York State commission charged with making executions more humane came up with the electric chair. Its first victim, in 1890, twitched for half a minute after being pronounced dead, Ms. Denno wrote.

The U.S. Supreme Court has never invalidated an execution method. In 2018, it set a standard that the chosen method cannot “superadd” terror, pain or disgrace, said Robin Maher, the executive director of the Death Penalty Information Center. But prisoners who object to the proposed execution method must provide a feasible and readily available alternative, the court said.

In that 2018 case, the prisoner, Russell Bucklew of Missouri, had already suggested nitrogen hypoxia as an alternative but had been rejected. He was not the only prisoner to try to choose nitrogen gas. In 2022, Richard Atwood, a death-row prisoner in Arizona, requested that the state use nitrogen in the gas chamber instead of cyanide. Cyanide executions had been described as prolonged and agonizing. And Mr. Atwood’s mother was Jewish and had fled the Nazis, who used a form of cyanide in their gas chambers.

The state refused the request, and Mr. Atwood died of lethal injection.

Proponents of nitrogen hypoxia have called it a painless and “nearly perfect” method of execution. But experts, including Dr. Philip Nitschke, a pioneer in assisted suicide who has witnessed dozens of nitrogen hypoxia deaths, warned of a risk of substantial suffering should things go wrong. Death penalty opponents argue that the method is experimental and could prove dangerous to those administering it. Nitrogen gas has caused deaths in industrial accidents and has been used in physician-assisted suicides but had never been tested in a death chamber before Thursday evening.

Even if the execution of Mr. Smith appeared to proceed without unintended consequences, death penalty opponents said that suffering could be hard to observe. Autopsies of people killed by lethal injection have suggested that their pain was masked, rather than reduced, by paralytics.