Every morning Damon Thibodeaux wakes up in his temporary digs in Minneapolis and wonders when his newfound freedom is going to come crashing down. "You think you're going to wake up and find it was just a dream," he says.

When he stepped out of Angola jail in Louisiana several guards were at the gate to wish him well, addressing him for the first time in 16 years as "Mr Thibodeaux". "No offence," he said, "but I hope I never see you again."

He walked out as the 300th prisoner in the US to be freed as a result of DNA testing and one of 18 exonerated from death row. With the help of science he has been proved innocent of a crime for which the state of Louisiana spent 15 years trying to kill him.

For those years Thibodeaux was in a cell 1.8 metres by 3 metres for 23 hours a day. His only luxury was a morning coffee, made using a handkerchief as a filter with coffee bought from the prison shop; his only consolation was reading reading the Bible; his only exercise pacing up and down for an hour a day in a the "exercise yard"– a metal cage slightly larger than his cell.

Like most death rows in the United States, the prisoners in Angola are treated as living dead things: they are going to be executed so why bother rehabilitating them? He watched as two of his fellow inmates were taken away to the death chamber, trying unsuccessfully not to dwell on his own impending execution. "It was like, one day they may be coming for you. At any time, a judge can sign an order and they can come and take you and kill you."

At the lowest point, he says he felt such hopelessness that he considered dropping all his appeals and giving up. He would become a "volunteer" – one of those prisoners who are assumed positively to want to die but so often simply lack the will to live. He read the Bible some more, shared his fears with other prisoners through the bars and found a new resolution. "I came to terms with the fact that I was going to die for something I didn't do. Truthfully, we're all going to die anyway; it made it a lot easier."

With little hope, he pressed on with his appeals and, almost imperceptibly at first, fortune's wheel began to turn. A lawyer assigned to his post-conviction appeal became concerned by his case, and she in turn enlisted the help of the Innocence Project in New York, a national group devoted to exonerating wrongfully convicted people through DNA testing.

Also drawn into the fray were a pair of Minneapolis-based lawyers from the commercial firm Fredrikson & Byron. In his day job Steven Kaplan works on mergers and acquisitions, not rape and murder, but he threw himself at the Thibodeaux case pro bono.

As soon as Kaplan began reading the legal papers relating to Thibodeaux's death sentence, he was astonished. He had never worked on a capital case before and, like most people unversed in the finer details of the death penalty in America, had assumed that the judicial process must have adhered to the very highest legal standards. After all, a man's life was at stake.

"When I read the transcript of the trial for the first time, I thought to myself that the high school mock trial team that I coached of 15- to 17-year-olds would have run rings around the lawyers in that courtroom," said Kaplan. "We put more energy into a $50,000 contract dispute than went into the defence at the Damon Thibodeaux trial."

The sequence of events that put Thibodeaux on to death row began on 19 July 1996. He was 22 and worked as a deckhand on Mississippi river barges.

Two weeks earlier he had moved back to New Orleans, where his mother and sister lived, to help out with his sister's wedding. He started hanging out with the Champagne family, distant relatives, who had a flat in a neighbouring suburb.

He spent 19 July at the Champagne home with the father, CJ, mother, Dawn, and 14-year-old daughter, Crystal. At about 5pm Crystal asked Thibodeaux to go with her to the local Winn-Dixie supermarket but he was busy mending CJ's watch. She left the house on her own at 5.15pm.

When she was not back more than an hour later her mother became alarmed and they began a search, Thibodeaux joining the effort. They called the police and searched through the night and through the following day.

It was not until after 6pm on 20 July that Thibodeaux went back to his mother's house and lay down to rest. He was just falling asleep when police arrived and asked him to come with them.

That was at 7.32pm. At 7.40pm Crystal's body was found on the banks of the Mississippi, about five miles from the Champagnes' home. The news was transmitted to the detectives quizzing Thibodeaux and instantly a routine missing-person interview became a homicide interrogation.

It started lightly, then the detectives began piling on the pressure. They repeatedly told him he was lying, putting their faces close up to his. When he gave them the names of the people he had been with over the previous 24 hours as alibis, the officers said they had talked to the individuals who had denied it. "That felt like I was being abandoned, because they were the only people who could put me in their presence away from the crime scene," Thibodeaux said. The police gave him a lie-detector test. When they returned to the interview room and told him he had failed, he fainted.

Several hours into the interrogation, they delivered the coup de grace: they warned him what would happen if he kept on lying. "They described to me death by lethal injection: organs collapsing, the brain shutting down, extreme pain. That's what they said would happen to me if I didn't give them what they wanted."

The detectives who interrogated Thibodeaux have consistently denied using techniques that put pressure on him. But having studied the case for years, his current lawyers are convinced he was subjected to a prolonged questioning that interacted with his vulnerabilities and broke down his resistance. About 4am on 21 July he gave the police what he thought they wanted. He had been under interrogation for nine hours, and had no meaningful sleep for 35 hours. "I had no sleep, I was hungry, I was tired of it. At that point I didn't care, I just wanted to stop it."

He began to confess, repeating details of the crime scene that the detectives had given him. "I'm not the smartest person on the planet, but I was able to figure out how Crystal died and how she was found from what they were telling me. I just put the pieces together and gave them the confession they wanted."

He told them how he had picked up Crystal in his car and driven her to the crime scene. They began having sex, then she asked him to stop and he refused. He raped her, hit her on the face with his bare hand, squeezing her neck and strangling her with a length of white, grey or black speaker wire that he procured from his car.

At one point Thibodeaux told his interrogators: "I didn't know that I had done it, but I done it." Case closed.

Within three hours of his confession, details emerged that refuted key aspects. Examination of the crime scene determined the cord that had been wrapped around Crystal's neck was a red electrical conductor wire that had been hanging on a nearby tree, and not the speaker wire Thibodeaux had confessed to. Crystal's mother also told investigators within three hours of the confession that Thibodeaux had been with her in the their flat when she called the police to report her daughter's disappearance – undermining any possibility of him getting to and from the crime scene in time to have murdered Crystal.

Further evidence came out that punctured his confession. The autopsy found that Crystal had been hit around the face with a blunt object, not Thibodeaux's bare hand as he had testified. Contrary to his statement that he had had sex with her and then raped her, the forensic examiner observed no injuries consistent with violent rape. More than that, he concluded that Crystal had had no sexual intercourse of any kind, consensual or otherwise, for at least 24 hours before she died.

All those discrepancies were known to the authorities before Thibodeaux was put in the dock for murder and rape. They also knew that there were other potential suspects who conceivably merited further investigation.

One individual was a local man with a conviction for paedophilia. Another was a relative of Crystal's who lived in a flat two blocks from the crime scene – a paranoid schizophrenic with a long history of drug abuse and violence against women.

Being poor, Thibodeaux could not afford his own lawyer and was assigned a public defence attorney by the courts. His attorney happened to be a former detective who had retrained as a lawyer, and this was his first murder case. At the time of the trial he was, unbeknown to Thibodeaux, applying for a transfer to the same district attorney's office that was prosecuting his client.

"I was willing to overlook the fact that he was an ex-detective," Thibodeaux says now. "But if I had known my lawyer was filing to be transferred to the DA's office I would have asked to have him removed from my case."

The trial lasted just three days. Over the course of it the prosecution tried to explain away the lack of any evidence of sexual intercourse or rape on Crystal's body by speculating that "semen-destroying maggots" had been at work.

Thibodeaux's lawyer, for his part, did not even refer to the confession. "You will read the entire trial transcript and he never utters the word 'confession', as though if he didn't mention it, it would go away," Kaplan says.

The jury was out for just 45 minutes before they delivered a guilty verdict. The next day the same jury sentenced Thibodeaux to death for murder and aggravated rape, even though no rape – indeed no sexual contact of any sort – had taken place.

It took Kaplan and the other lawyers just a few days to spot the glaring problems with the prosecution of Thibodeaux. It took them a further 12 years to free him. With the full co-operation of the current district attorney for New Orleans, they carried out a fresh round of DNA tests using world-renowned forensic scientists, such as Dr Henry Lee, who heads a forensic science school at the University of New Haven, and Dr Edward Blake, of Forensic Science Associates. They looked again at all the physical evidence, particularly the clothing of Crystal and Thibodeaux on the day of her murder. They found there was no evidence of Thibodeaux's tissue, blood or fluids on Crystal's clothing and none of hers on his – a significant finding as had Thibodeaux been the murderer and/or rapist, such evidence would certainly have existed.

In addition, witnesses were tracked down who gave him a watertight alibi for all but five minutes of the period between Crystal's disappearance and the time of her death. And lest there be any remaining doubt, a forensic expert on maggots – such people do exist – testified that the theory of "semen-destroying maggots" was balderdash.

Since his release Thibodeaux has travelled to the other end of the Mississippi to rebuild his life with the help of his new lawyers in Minneapolis. The town has a good rehabilitation programme that should provide a cheap home, renewed education and job training.

His 15 years on death row opened his eyes, he says. "We tell the world that our system is the best in the world, and it's not." But he says he still supports capital punishment in America for the most heinous cases – with the proviso that the conviction is sound.

Not so Steven Kaplan. He cites academic studies that suggest that 2% to 4% of death-row inmates are probably innocent. "If that was the rate of failure of airplanes," he says, "would you fly?"

Just another reason I'm for life imprionment vs. death penalty. You can at least correct a mistake with the former.