The hearing stems from a routine argument defense lawyers make in most death penalty cases. Judges rarely grant the motion, however, because the Supreme Court has repeatedly upheld the death penalty as outside of the ban on cruel and unusual punishment.
But Judge Kevin Fine, a Democrat elected last year, shocked many Texans by giving the argument serious consideration. As a result, his courtroom in downtown Houston became a forum Monday for defense lawyers to present a broad indictment of problems in the criminal justice system that they say lead to wrongful convictions.
They said that they hoped to prove that some of the biggest tools in the prosecution's arsenal were frequently unreliable and led to mistaken convictions: eyewitness testimony, fingerprint evidences and the testimony of informers.
Alan Curry, the chief of the appellate division in the Harris County District Attorney's Office, argued that the hearing should not be held and announced his office would not participate.
He declined to cross-examine witnesses. The prosecution has claimed that Judge Fine is biased against the death penalty and moved to remove him from the case, but the highest criminal court denied the motion.
Before the hearing started, Mr. Curry argued that the Supreme Court had already ruled that the risk of an innocent person might be executed did not make the death penalty unconstitutional. He also said Mr. Green had no standing to challenge the law, since he had yet to be convicted.
Mr. Curry argued that the fact that some innocent people had been wrongly convicted and condemned to death did not mean the evidence in Mr. Green's case was faulty.
But Richard Burr, one of the defendant's lawyers, said wrongful convictions happened so frequently in Texas that Mr. Green was at serious risk of ending up on death row. He also said the chances of overturning a bad conviction on appeal were low in Texas, which requires a defendant to show “no reasonable juror” would have convicted him.
“There is no safety net,” Mr. Burr said.
Still, Judge Fine, a maverick former defense attorney who talks openly of his past as a recovering alcoholic and has tattoos depicting his struggle with addiction, ruled the hearing should go forward.
To prevail, the defense must show the death penalty statute in Texas violates the Eighth Amendment ban on cruel and unusual punishment because it creates a risk that innocent people will be convicted and put to death.
Texas has executed 464 people for murder in the last three decades, more than any other state, and the death penalty has widespread support here. But in at least 12 cases since 1973, people on death row in Texas have been exonerated. In addition, questions have been raised about the convictions of two men already executed for their crimes — Cameron Todd Willingham and Claude Jones.
Mr. Willingham was put to death in 2004 after being convicted of burning down his home in Corsicana in 1991, killing his three children. His guilt is now in question as arson experts have found fault in the evidence against him. Mr. Jones was executed in 2000 for the 1989 killing of a liquor store owner near Point Blank. After his death, a DNA test showed that a hair that had linked him to the crime scene did not belong to him.
Both cases are expected to be raised during the hearing.
Richard C. Dieter, the director of the Death Penalty Information Center in Washington, was the first witness. He said that since 1973, at least 138 people sentenced to death had been later exonerated. “There certainly is a risk of executing the innocent and that risk still exists today,” he said.
“The mistakes are happening at the trial level,” Mr. Dieter said. “And then you get into the appellate level where the focus is on legal problems that might have occurred, not on whether you got the right person.” | 
