He was a lifelong criminal, with a rap sheet that included a murder conviction for setting fire to a fellow inmate in a Kansas prison. Two eyewitnesses and his accomplices placed him at the liquor store. And even one of Jones' attorneys says the defense had "a devil of a time finding a good character witness."
But there are new questions 10 years after Jones was executed about whether he actually killed 44-year-old Allen Hilzendager while robbing the store, and whether the testimony used to convict him was enough. A judge has ordered DNA testing on a strand of hair that prosecutors used to link Jones to the murder.
It's the second time in a year the guilt of an executed Texas inmate is in doubt. A fire expert last year said the investigation of the fire that killed Cameron Todd Willingham's three daughters was so flawed that the arson finding can't be supported. Willingham was executed in 2004. Last month, a state panel concluded that arson investigators were not negligent.
"He was no poster boy, Claude," said Jerald Crow, Jones' trial attorney. "But that doesn't matter. The law is the law, and they need to follow it."
Under Texas law, a defendant can't be convicted on accomplice testimony without corroborating evidence. The hair collected from the liquor store was the key evidence supporting the testimony of an accomplice who implicated Jones.
A DNA test that shows the hair came from someone else wouldn't exonerate Jones. But it could show the state didn't have enough to convict or execute Jones, who was put to death in 2000 at age 60.
Whether the hair was Jones' is irrelevant to Hilzendager's three surviving siblings, who live in separate homes on the family's old dairy farm. Allen's house, tucked among the trees, remains half-finished.
"There's no doubt in my mind he did it," said Joe Hilzendager Jr., 73.
Jones was guilty of plenty. Before his 20th birthday, he already was serving nine years for burglary, theft and robbery by assault. Over the next nine years, he added theft, first-degree robbery and possession of a firearm to his record.
A change of scenery didn't help. A Kansas court sentenced him to 21 years behind bars, and it was in a Kansas prison that he poured a flammable liquid on a man and set him ablaze. He was sentenced to life in prison.
But by 1989, Jones was free on parole, back in Texas and hanging out with ex-con Danny Dixon, who authorities say shot a girl between the eyes and buried her in a cemetery.
They decided to rob the liquor store located just outside of Point Blank, population 559, on a rural road near the Sam Houston National Forest. Besides selling booze, Hilzendager cashed paychecks for customers. That meant he had a lot of money in the store.
Court documents and police records tell the story.
Jones, Dixon and another man drove up to the store, where Hilzendager was outside loading boxes into his vehicle. Jones got out, put his arm around Hilzendager and escorted him inside.
The first shot was to the back, severing an artery and puncturing a lung. The second hit Hilzendager in the right shoulder, likely as he was holding up his hands. The third struck him in the side as he lay on the ground.
A puddle of red spread around Hilzendager, soaking his jeans and blue plaid shirt. Blood dripped down a bottle of Seagram's gin and splattered the wall behind the shelf of Crown Royal.
Jones cleaned out the register, not seeing two bank bags stuffed with $7,000 and a firearm beneath the counter. He walked out, changed his mind and returned for a bottle of whiskey. Then the three men left.
Two witnesses, who were fixing a car across the street, identified the heavyset Jones. But it was something else that convinced Sheriff Lacy Rogers of the identity of the triggerman.
"Claude Jones was definitely the shooter," Rogers said. "(Dixon) would shoot you if you pulled a gun or something. Yeah, he'd shoot you. But Danny Dixon is not the kind of guy that shoots you in the back."
Jones was arrested less than a month later in Florida after robbing a bank. Dixon led the sheriff to the gun, which he had ditched in the Trinity River. A forensics expert said a strand of hair in the store could have come from Jones but not from the other men.
Prosecutors also hammered home Jones' brutal past. A jury quickly convicted him. The Texas Court of Criminal Appeals barely upheld the conviction with a 4-3 vote.
Judge Charles Baird said the case relied too strongly on the testimony of the accomplice, "who seemed entirely capable of committing the crime himself."
"There was just something in my gut that told me this didn't pass the smell test," Baird said. "I was always afraid this was an innocent guy on death row."
Seven state and federal courts reviewed Jones' case, and none halted the execution.
Jones' final statement was an apology, but not a confession.
"To your family, ah, I hope that this can bring some closure to y'all," he said. "I am sorry for your loss and hey, I love all y'all. Let's go."
But up to his death, he denied being the triggerman to his lawyer and his son. Duane Jones of Houston said his father freely confessed to all of his past crimes. Just not this one.
The hair is being tested because Duane Jones -- along with the Innocence Project, other innocence groups and The Texas Observer magazine -- sought temporary restraining orders preventing its destruction.
"If you are going to be the execution capital of the free world, then you should take every opportunity available to make sure the system is above reproach," Duane Jones said.