The idea of lethal injection has been around since 1888, when New York State first considered the method and doctors strenuously opposed it, fearing that the public would associate medicine with death. Oklahoma revived the idea of lethal injection in 1977 when — with the state’s electric chair broken and requiring expensive repair and with Gary Gilmore’s recent firing-squad execution in Utah having created an unsavory spectacle of state violence — the state’s chief medical examiner, Jay Chapman, after being approached by a state representative, devised an execution method that mimicked the induction of general anesthesia. When I met Chapman at his house in Santa Rosa, Calif., he described himself to me as “an expert in matters after death but not in getting people that way.” Nonetheless, in 1977 the Oklahoma Legislature ratified a bill that incorporated the general description of a method he proposed. Over the subsequent decades, 36 other death-penalty states came up with some version of Chapman’s method.

Deborah Denno, a professor at Fordham University Law School, says that what she thinks of as America’s deep ambivalence about capital punishment — our inability to do away with it or to think very hard about it — has meant that Chapman’s story, that of one man making a small and modestly considered proposal that then persists over time, is not unique. “The history of the death penalty in America is full of people getting involved and not realizing that what they contribute is going to be stretched to the limit,” Denno told me. In 2001, Denno conducted an extensive survey of lethal-injection protocols. She found that many states made errors when creating their own protocols by using drugs that Chapman originally suggested. As Denno wrote in 2002 in The Ohio State Law Journal, “One of the most striking aspects of studying lethal-injection protocols concerns the sheer difficulty involved in acquiring” those protocols. She found that only one-quarter of the states that used lethal injection specified the quantities of the drugs to be injected.

Chapman’s method works like this: The execution team inserts an IV line, and then the condemned is given sodium pentothal, the first of three drugs. Sodium pentothal, classified as an “ultrashort-acting barbiturate,” is meant to render the inmate deeply unconscious within 90 seconds. A second drug, pancuronium bromide, a muscle relaxant or paralytic (it paralyzes all skeletal muscles, including the diaphragm), keeps the inmate from disturbing the witnesses by gasping, moaning or flopping around on the gurney. The third drug, concentrated potassium chloride, stops the heart.

The technique utilizes medical equipment, knowledge and technique as well as medicine’s veneer of respectability. If performed correctly, without human error, it should kill inmates quickly and painlessly. Yet each of the four main steps involved — securing IV access and then injecting each of the three drugs — has raised medical concerns. Starting an IV can be very difficult on a person who is obese, nervous or cold or who has a history of IV drug use, any one of which is not an unlikely complication in an inmate about to killed. Sodium pentothal is not packaged in solution, meaning the executioners must mix the powder with water just before killing, a somewhat delicate thing to do. The pancuronium bromide, or paralytic, prevents observers from determining if the inmate is properly anesthetized, since he can’t speak or move. Potassium chloride, which stops the heart, creates a burning sensation in the veins and might cause excruciating pain if the inmate is not properly anesthetized. (These concerns, and others, appear in the 1953 British report.)

Under careful medical supervision, these problems, most likely, would rarely have arisen. But in 1980, between the time Chapman devised his lethal-injection method and the time Texas first used lethal injection to execute an inmate, the American Medical Association in its ethics code told its members not to participate in executions (though that mandate has not been strictly enforced). Later the code would prohibit physicians from selecting fatal-injection sites or starting IV lines; prescribing or injecting lethal drugs; inspecting, testing or maintaining lethal-injection equipment; consulting with or supervising an execution team; monitoring condemned prisoners’ vital signs; or declaring the death of the inmate. (Confirming or certifying after an inmate has been declared dead is permissible.) As a result, the first execution by lethal injection — that of Charles Brooks Jr. in Texas in 1982 — did not go well. The execution team turned to a doctor, who had come only to certify the death, in order to find a suitable vein for the IV. Instead of preparing and injecting each of the three drugs separately, the warden mixed them all in the same syringe, producing a thick, white sludge. When the attending doctor approached Brooks to certify death, he found the inmate still breathing. The task of administering drugs, so routine in hospitals, failed to translate smoothly to the death chamber. As Chapman, its progenitor, told me: “It never occurred to me when we set this up that we’d have complete idiots administering the drugs.”

A week after Doerhoff’s testimony in the Taylor case in Missouri, in the presence of the mothers of both the condemned man and the murdered girl, Dr. Mark Heath and Dr. Mark Dershwitz took the stand. The arguments over lethal injection’s constitutionality are largely medical, and both doctors have had busy years testifying or providing affidavits in many states with a lethal-injection proceeding. Dershwitz, a professor of anesthesiology at the University of Massachusetts Medical School and an expert witness for the state, told the court that in his professional opinion, the five grams of sodium pentothal Doerhoff claimed to typically administer to condemned inmates would render a person unconscious 99.99999999 percent of the time, assuming the drug went through a working IV line. According to Dershwitz, most people who received such a dose would remain unconscious for 13 hours, if they were able to continue breathing. A third of that dose, 1.67 grams of sodium pentothal, should produce a deep state of unconsciousness in almost anyone. “It all boils down to the skill level at getting a functioning IV in, and you don’t need a lot of fancy initials after your name to do that,” Dershwitz told me. A rough gauge of unconsciousness is not difficult either. “Have you ever taken a CPR class?” he asked. “What’s the first thing they teach you: you shake the doll and say, ‘Annie, Annie, are you O.K.?’ If Annie doesn’t respond, she’s not conscious.”