Buntion's original death sentence was overturned because of a problem with jury instructions, and prosecutors say if this new trial doesn't result in him being sent back to death row, he could eventually be paroled.
There is a big police presence in the courtroom as prosecutors try to convince a jury that Buntion should be executed.
While Buntion sat in prison for the last 22 years, the family of James Irby, the Houston police officer he killed, has had to endure appeals, reversals, and now faces a retrial in which the jury can take him off of death row, changing his sentence to life in prison.
In 1990, Buntion shot Officer Irby in the head during a traffic stop. At the time, Texas did not have life without parole and the jury gave him a death sentence. Even though there is now life without parole, the 1990 laws still apply. That means a parole board could let him out.
According to Buntion's lawyer, the now 68-year-old convicted killer has been a model prisoner. He says that his behavior behind bars along with mitigating circumstances not presented at the first trial -- including Buntion's mental illness and troubled childhood -- should keep him off of death row.
Our legal analyst, Joel Androphy, says jurors have a simple question to answer.
"The issue that jurors will be deciding is if he spends the rest of his life in prison or put to death," said Androphy. "He's never going to get out on the streets of Harris County."
Officer Irby's widow and 25-year-old son, who is himself a police officer, are disappointed and hope this jury will choose the death penalty.
"He was kind, he was generous -- generous to a fault. He was the kind of man that if your car broke down in the middle of the night in Galveston and he had to drive from Conroe to Galveston, he would do it. He cared a lot about what he did," said Maura Irby, widow of Officer Irby,
'We'll present evidence of that from his family that will come in and testify to things that weren't testified in the first trial about an incredibly abusive childhood that he had and a terribly abusive, alcoholic father who was extremely violent in ways that I don't want to say on TV," said Casey Keirnan, attorney for Buntion.
If Buntion gets life in prison the Irbys say they will be tortured by having to go to the parole board for years to testify that he should stay in prison.
This trial could take three weeks.