Until a judge told them to stop last week, penal authorities in Arkansas planned to kill seven people in 11 days. All seven were convicted of horrible crimes and sentenced to die by the state; put aside how you feel about that for a moment. What’s salient here is how those men are supposed to die—the execution of their executions.

According to Arkansas’ Lethal Injection Procedure, each man will first get an intravenous injection of a sedative called midazolam, a benzodiazepene—the same class of drugs as Valium. On death row it’s supposed to induce a deep, insensate coma.

Then comes a dose of vecuronium bromide. Technically that’s a nonpolarizing neuromuscular blocker, a muscle relaxant. On death row, it’s a paralytic, intended to keep the prisoner still and, maybe, to suffocate. If you can’t move your diaphragm, you can’t inhale.

All that’s just a wind-up for the real kill shot: potassium chloride. The potassium ion messes up the electrical properties of the cells of the heart, making it impossible for them to contract. The heart stops beating.

Not every state executes prisoners the same way. Some only use one drug, or follow different protocols. But the idea, everywhere, is the same: to execute people without violating the Constitution’s Eighth Amendment protections against cruel and unusual punishment. In fact, the whole point of lethal injection was that it seems like a more humane way of executing someone than hanging, shooting, head-chopping-off, gas chambers, stuff like that.

The problem is, no one knows if lethal injection really is more humane. In court case after court case, lawyers have argued that botched executions by lethal injection show that it’s a painful and faulty method. What little research exists hints at the same conclusion. No matter how you feel about the fact that the criminal justice system sometimes kills people, even innocent people, you have to also feel something about the fact that the criminal justice system isn’t very good at killing people.

Execution Isn’t Easy

An Oklahoma medical examiner named Jay Chapman pitched the three-drug protocol in 1977—without a single study or piece of scientific evidence. But hey, it definitely killed people, and executed them less disgustingly than poison gas or gunshots. “No one has done any peer-reviewed experimental research into the mechanisms of death by lethal injection,” says Teresa Zimmers, a researcher at Indiana University’s School of Medicine and one of the few people to publish research on the practice. “That, of course, is because support for the death penalty in the US has generally rested on the fact that people perceive lethal injection to be humane.”

Chapman’s original protocol called for a tranquilizer from the barbiturate family. But by the 2000s, barbiturates were in short supply. Drug companies find the use of their medicines as engines of death to be distressingly off-brand, barbiturates were falling out of favor as anesthetics, and all of Europe had prohibited the use of those drugs in executions, shrinking the market.

That forced states to search for an alternative. Ohio landed on the sedative midazolam, and Florida started using it in 2013. The problem is, midazolam turns out to be a terrible coma-inducer. Prisoners were waking up mid-execution, coughing and snoring. “It’s not even close to being an appropriate drug for executions,” says Robert Dunham, executive director of the Death Penalty Information Center. “But when states were no longer able to get ahold of anesthetic for use in executions, they casually looked around to see what else doctors use to put somebody to sleep.”

The thing is, when you’re being executed with a three-drug protocol, you really want to be knocked out. That second drug, the paralytic, is probably extraordinarily painful the whole time you’re suffocating—except no one can tell, because, well, you’re totally paralyzed. (Fun side note: The paralytics are typically synthetic versions of curare.) The potassium chloride injection burns like fire. And even with a barbiturate on board, people might feel all of that every time.

The Search for a New Necrology

These gaps in knowledge seem fillable, but states have been less than transparent about their practices, and scientists haven't wanted to look too closely at lethal injection. “It’s either that they don’t know too much about the science, or that they’re not telling us,” says Megan McCracken, an attorney at UC Berkeley’s Death Penalty Clinic who specializes in Eighth Amendment challenges. “As lawyers, we want to know, how did the state come up with a drug formula? Who told them, or with whom did they consult, to come up with this dose and this timing? And those questions they decline to disclose.”

Even if states wanted to know more about anesthesia for executions, the anesthesiologists themselves couldn’t help. In general, big medical societies like the American Medical Association prohibit their members from studying or helping with executions. “It’s inherently unethical to conduct experiments on how to best execute people,” says Dunham. “And the people best qualified won’t do it because it’s a clear violation of the Hippocratic oath.” One of the lethal injection researchers I called for this story declined even to comment on the subject.

You could imagine the set-up for a study to look at how lethal injection drugs work, or might work better—depending on your definition of “better,” of course. Maybe an institutional review board (a group that approves the ethics of study designs) would allow condemned prisoners to consent to analyses of their responses. Or maybe not; the so-called Common Rule that protects human research subjects singles out prisoners for special protections, having already been deprived of various rights.

Or you could look to other literature on chemically-caused death. Some states in the US allow physician-assisted suicide, for example. The Netherlands allows euthanasia. But having a Dutch doctor standing by your bedside as you slip into a coma you asked for is pretty different from someone pumping drugs from a separate room through 20 feet of tubing. Veterinary protocols for large-mammal euthanasia might be helpful, too, but they usually have more to do with keeping handlers alive while trying to kill a dangerous animal. Oh, and the veterinarians want about as much to do with executing humans as physicians do.

In a final cruel and unusual twist, a subsidiary finding in Glossip v. Gross—the same 2015 Supreme Court decision that said it was OK if execution methods caused pain and gave the go-ahead to using midazolam—said that any challenge based on Eighth Amendment rights had to include an alternative execution method. It was basically the equivalent of saying that if you don’t want to incriminate yourself in courtroom testimony, you have to incriminate someone else. (Do it to Julia! Not me!)

That’s a problem, because the science to figure out that better alternative doesn’t exist. Still, some states have started advocating execution methods beyond lethal injection anyway. Utah is looking at the firing squad. (A classic!) Louisiana officials have talked about a gas chamber using nitrogen, which is either a death as peaceful as falling asleep or just like drowning. No one knows for sure. And for those half-dozen men on Arkansas’ death row, it’s too late to find out.