A little after 4 a.m. on July 21, 1996, Damon Thibodeaux, a deckhand on a Mississippi River workboat, cracked at the end of a nine-hour interrogation and confessed to the brutal rape and murder of his 14-year-old step-cousin, Crystal Champagne.

“I didn’t know that I had done it,” Thibodeaux said at one point, according to a police transcript. “But I done it.”

Before that day was over, Thibodeaux had recanted his confession, telling his court-appointed lawyer that he told police what they wanted to hear in response to threats of death by lethal injection and his grief over the death of his cousin. Nonetheless, Thibodeaux was later convicted of both crimes and sentenced to die.

Now, after more than 15 years spending 23 hours a day in solitary confinement on death row at Louisiana’s Angola prison farm, Thibodeaux is free.

Judge Patrick McCabe — who presided over the original trial in 1997 — issued a sealed order on Thursday vacating the conviction. With Thibodeaux’s release Friday, he became the 300th wrongly convicted person and 18th death-row inmate exonerated in the United States substantially on the basis of DNA evidence, according to the New York-based Innocence Project, which provides legal counsel to prisoners it believes can be exonerated through DNA testing.

Friday’s release was authorized by Jefferson Parish District Attorney Paul Connick Jr. after an extraordinary five-year joint re­investigation with defense lawyers concluded that the murder confession was clearly false. Nearly every ostensible fact in the statement didn’t match the crime scene or other evidence. The inquiry found that the sexual assault to which Thibodeaux also confessed — making him eligible under Louisiana law for the death penalty — never occurred.

The Thibodeaux case marks a dramatic mathematical milestone in the use of DNA in law enforcement, but it also signals the opening of a new, more complex phase in the use of such material in attempts to right the course of justice.

When DNA testing was first introduced in the late 1980s, the revolutionary new techniques shattered a widely held view in law enforcement and the public that American courts rarely convicted the innocent. Since then, high-profile exonerations and the increasingly common reliance on such testing have led many to believe that DNA can resolve doubts about almost any questionable conviction.

It’s now clear, however, that there is no DNA evidence in the vast majority of cases. In the first 15 years of DNA testing, almost all exonerations fit a basic pattern in which the defendant was accused of rape, or both rape and murder — because sexual assaults are the crimes in which DNA is most likely to be recovered. Between 1989 and the end of 2007, a total of 214 people were cleared using DNA evidence. In all but 14 cases — more than 93 percent — the alleged crime involved a sexual assault of some kind, according to a review by The Washington Post.

In hindsight, those straightforward, obvious miscarriages of justice were the low-hanging fruit of DNA exonerations. Now their numbers are declining. In their place are convictions such as Thibodeaux’s, in which serious doubts have been raised but little clear DNA or other scientific forensic evidence exists to conclusively prove guilt or innocence. In Thibodeaux’s case, the absence of any incriminating DNA evidence became as powerful an argument for his innocence as any other element of the case.

Of 83 exonerations in the past five years, more than 15 percent didn’t involve rape. As many as a quarter of the cases involved a false confession, in which one or more defendants admitted to the crime under interrogation.

Samuel Gross, an author of a report by the recently created National Registry of Exonerations at the University of Michigan, calculated that based on the proven rate of exonerations among death-row prisoners in the past two decades, U.S. courts appear to have an error rate in capital cases of between 2.5 percent and 4 percent. In June, researchers examining biological evidence from hundreds of Virginia rape convictions between 1973 and 1987 determined that new DNA testing appeared to exonerate convicted defendants in 8 percent to 15 percent of cases.

Applied against the approximately 140,000 prisoners on death row or serving life sentences in the United States, the findings suggest that many thousands of innocent individuals could be in prison for crimes they didn’t commit.

But the odds that many of those convicts will ever be able to prove their innocence through the existing systems of appeals are remote, given the lack of DNA evidence in the majority of cases.

That was largely true for Thibodeaux. In the hours after Champagne disappeared on July 19, 1996, there was no evidence to suspect Thibodeaux. The 14-year-old lived with her mother and other family members in an apartment complex on the frayed blue-collar edges of New Orleans. Her uncle had once been married to Damon Thibodeaux’s mother, making them what the families called “step-cousins.”

In the initial investigation of Thibodeaux, police found no physical evidence linking him to the crime. Since the victim had in fact not been sexually assaulted, there was also none of the DNA typically associated with a rape.

The only strong evidence against Thibodeaux was his confession. He never asked for legal representation. Early in the questioning, a detective asked at least a dozen times whether he had been involved in the killing, according to partial transcripts. “No sir,” Thibodeaux said firmly each time. After denying any involvement in the crime for more than six hours, an almost catatonic Thibodeaux confessed to police just before dawn. Almost every factual assertion he made was plainly incorrect.

“At that point I was tired,” Thibodeaux said, in an interview minutes after his release Friday. “I was hungry. All I wanted to do was sleep, and I was willing to tell them anything they wanted me to tell them if it would get me out of that interrogation room.” He said investigators fed him details of the crime scene. His salvation was that many of those details were incorrect.

The lack of conclusive DNA evidence in Thibodeaux’s case was overcome only through the unusual joint investigation between the district attorney and defense lawyers — during which Thibodeaux, now 38, put his formal court appeals on hold.

The inquiry found glaring contradictions between the confession and physical evidence. New DNA testing conducted on clothing worn by Thibodeaux on the night of the killing and virtually every other piece of evidence established no links to the crime. A DNA profile was obtained from a tiny sample of blood on a piece of wire used to strangle the victim. It didn’t match Thibodeaux. The cost of the reinvestigation was more than $500,000, shared by the defense and prosecution, according to lawyers involved in the case.

Thibodeaux, who plans to move to Minnesota to restart his life, didn’t sound bitter after his release Friday, but rather relieved. “Right now, I’m just adjusting to being not behind bars,” he said, “and not being told where to go, what time to go. Getting used to not having chains on. That’s a novelty for me.”