OVER the last few weeks the controversial issue of the death penalty has once again been in the spotlight.

This comes in the wake of a report by the human rights group, Amnesty International, that says there was a surge in the number of executions carried out worldwide in 2011. Only last week Japan sent three men to the gallows, ending a 20-month moratorium and effectively terminating a nascent debate on the country's death penalty. According to the latest Amnesty review, at least 676 people were executed in 20 countries in 2011, compared with 527 in 23 countries in 2010.

Amnesty no longer publishes figures for China, where the data is considered a state secret. The rights group believes the figure to be in the thousands. Elsewhere, the number of confirmed executions in the Middle East rose by almost 50%, to 558. The group also condemned as "shameful" the US's use of the death penalty, noting that it was the only Western democracy to execute prisoners last year, 43 in total, ranking the US as fifth in the world for capital punishment.

THE Montgomery County Courthouse is in the heart of old Conroe, just past the Crighton Theatre, across the street from the Masonic Lodge. Founded at the junction of two great railroads, the town was transformed by a 1930s oil boom that briefly made it one of the richest communities in the United States. These days it is a prosperous exurb, at the edge of Houston's sprawl. Freight trains whistle as they pass through.

In the corridor leading to the Ninth District Court, there are sepia portraits of former justices. By the door, there is a picture of the incumbent, Judge Fred Edwards, arm in arm with President George HW Bush, plus a photograph of President Bush the younger, thanking Edwards for his service.

Larry Swearingen has been in this courtroom before, three times, accused of raping and murdering a pretty college student, Melissa Trotter. After each appearance a date has been set for Swearingen to be strapped to a stretcher and injected with drugs: sodium thiobarbital to anaesthetise him, pancurium bromide to paralyse his muscles and potassium chloride to stop his heart. The next date will be his last.

In January 2009, he had written his goodbyes and was on his way to the chamber when the stay of execution came through. "The way I had to look at it, was 'I'm just gonna lay down and go to sleep,'" he says. "I wasn't gonna grovel. I wasn't gonna sit there and cry. I can't be remorseful for a crime that I didn't commit."

Swearingen sits with his defence team, feet shackled together, wearing a striped Montgomery County Jail jumpsuit. He has spent the last 12 years in solitary confinement, in a cell not quite four metres long and a little over two metres wide, so the hearing is a break, of sorts.

In the pews on the right, behind the District Attorney's table, Sandy and Charlie Trotter are surrounded by supporters holding pictures of Melissa.

Pam Martinez, Swearingen's mother, has attended every day of the hearing, even though she has recently had heart surgery for the second time. "My cardiologist tells me that I need to cut the stress out," she says. "I would like to cut the stress, but I support my son. He's my child and I want to protect him."

Melissa Trotter disappeared on December 8, 1998. Swearingen was one of the last people seen with her, in the canteen at Montgomery College. Three days later police picked him up on outstanding arrest warrants, threw him in prison and began to build a case against him. In a missing persons' report, distributed a week later, he was named as the only suspect.

Trotter's body was discovered on January 2, 1999, in the Sam Houston National Forest, by hunters looking for a lost gun. At first glance, they thought it was a mannequin, dumped in the woods. She was wearing jeans, but her torso was naked. She had been strangled with one leg of a pair of tights. A search team, with cadaver dogs, had passed within 20 metres of the spot a fortnight earlier and found nothing.

Although there were signs of decomposition around Trotter's head, her corpse was in strikingly good condition. At the autopsy, with the District Attorney and two of his sheriffs in the room, Harris County's chief medical examiner, Dr Joye Carter, estimated that she had been dead for around 25 days, meaning she had been killed the day she went missing.

When Carter repeated this at the trial, the defence team let it pass unchallenged. Jurors heard that Swearingen had a history of violence towards women, that he had repeatedly lied to police, that he had fabricated a letter, from jail, full of details only the killer could know, in an attempt to confuse investigators. They heard that hairs forcibly removed from Trotter's head were recovered from his truck and that the other leg of the pair of tights used to kill her was found in his house.

They were not told that the tights appeared during a fourth police visit to the property, after three prior searches had turned up nothing so incriminating. Carter did not disclose that she had taken tissue samples from the internal organs, which were intact. The DNA under Trotter's fingernails, belonging to someone other than Swearingen, was dismissed as a contaminant – perhaps a drop of blood from a cut in a forensic technician's hand. The jury took less than two hours to sentence Swearingen to death.

The basis of Swearingen's defence is that forensic science provides him with an alibi: he cannot have murdered Trotter, because he was in prison when she was killed. The case was sent back to the Ninth District Court by the Texas Court of Criminal Appeals after Carter signed an affidavit stating that "internal findings support a forensic opinion that the body had not been exposed more than two weeks in the forest environment."

The chief medical examiner for Galveston County, Dr Stephen Pustilnik, testified for the defence. "For many days, where she was found, it was 20 degrees Celsius," he says. "If you're at that temperature for three days, you're green, bloated and stinky. Inside the body where the heat is held, the organs will decompose at a faster rate than the skin surface will. Her internal organs look beautiful." At the morgue, Trotter's body weighed 47.7kg. Alive, she had weighed less than two kilos more.

Using histology slides – slivers of Trotter's heart, lungs and spleen, examined under a microscope – the assistant medical examiner for Tarrant County, Lloyd White, estimated that she had been dead for less than a week when she was found. "Seven different forensic experts have now told the judicial system that Mr Swearingen could not have committed this crime," wrote Dr Harrell Gill-King, director of the Laboratory of Forensic Anthropology, in his brief to the court.

The problem for Swearingen is that their conclusions have been heard and dismissed before. Upholding the conviction, appeals court Judge Cathy Cochran concluded that: "The scientists are all over the board. Theirs is like the Indian tale of the blind men touching the various parts of the elephant and coming to entirely different conclusions about the animal."

Assistant District Attorney Warren Diepraam argues that balanced against the "overwhelming evidence of guilt" provided at trial, the forensics must be viewed sceptically. "The science that the defence is relying on is as scientific as people who believe that the earth is flat," he says. "The scientists have gone from being neutral observers to advocates on behalf of Mr Swearingen."

During the appeals process, the burden of proof shifts to the defence. To win a retrial, Swearingen's lawyer, Steve Jackson, must show that no reasonable jury would convict, based on clear and convincing evidence of his client's innocence. "It's almost impossible, you're trying to prove a negative," he says. "Judge Edwards will not grant a retrial. He's in an election year." On his campaign flyers, Edwards notes that he has never had a capital conviction overturned.

At the hearing, the judge is suffering from a cold that causes him to rest his head in his palm, or lie back in his burgundy leather chair, eyes closed, as if asleep. He frequently appears exasperated, cutting short lines of enquiry as "a waste of time", sustaining prosecution objections and dismissing the defence team's complaints.

At one point, he engages veteran forensic pathologist Dr Werner Spitz, who is testifying for the prosecution: "Is it common, 12 years after a death, to ask people to look at photographs and determine time of death? All these opinions that I'm getting, they never looked at the body."

"It's all second-guessing," replies Spitz, implying that forensic indicators of post mortem interval are too imprecise to be relied upon after the event. Only Carter's original estimate of "25 days or so", based on the external condition of the body alone, with the District Attorney looking over her shoulder, can be trusted.

Time and again, confronted with photographs of Trotter's notably intact organs, Carter declines to answer questions about what the pictures tell her. "You document what you find," she says. "It was 13 years ago." In the front row, Trotter's parents look away as the most graphic images are displayed. It must be torture, but they will see it through. When the defence presses Spitz for an opinion about a specific histology slide, the judge intervenes on his behalf. "There is only one person that has heard all the testimony at both the original trial and at all of these writ hearings. That's me," he says. "I can safely say that you cannot exclude things and just look at one sliver and say 'this is it.'"

Whatever Edwards rules, the Texas Court of Criminal Appeals will have the final word. The court, composed of nine elected judges, has ordered three retrials of capital cases in the last decade – although it has commuted many sentences to life without parole. The Presiding Judge, Sharon Keller, is best known for denying a 20-minute extension to a defence lawyer whose fax machine malfunctioned as he filed an appeal. His client was executed that night.

If the TCCA upholds Swearingen's conviction, he has run out of options. His "actual innocence" petition to the Supreme Court has been denied. Any further appeals will be summarily rejected. A new execution date will be set and, barring an unprecedented last-minute pardon, he will be taken to the execution chamber at Huntsville and put down.

Swearingen knows his chances are slim. "Under federal law in the United States being innocent does not matter," he says. "If being innocent makes no difference, this country is no better than Iran or Syria, these third-world countries that kill their own citizens. How can being innocent not matter?"

I ask his mother whether she is reconciled to the fact that he will, in all likelihood, be executed. "I have buried two husbands, both my parents, and I'm ready to make sure my son is taken care of before I leave this earth," she says. "That's why I fight so hard to stay alive. I've already told him, and I will go to heaven when it's our time and he'll be judged by the Lord, not by the people of Montgomery County."