HOUSTON — A Texas jury took only 17 minutes to convict parolee and former mechanic Duane Buck of gunning down his ex-girlfriend and a man at her Houston apartment, then deliberated about four hours before deciding he should be put to death.

Now nearly two decades later, the U.S. Supreme Court is being asked to look for a third time at whether the death sentence the jury gave Buck was tainted by testimony and evidence related to the fact he is black.

“Injecting race into a capital sentencing proceeding is not only wholly improper, it poses a special risk of harm to the defendant, and one that, respectfully, this Court cannot — and must not — tolerate,” Buck’s lawyers said in briefs submitted ahead of Wednesday’s scheduled arguments before the high court. They have been fighting for years to get a new punishment hearing.

Buck’s case doesn’t present a broad challenge to the death penalty but draws attention due to Texas’ standing as the nation’s leader, by far, in carrying out 537 executions since the Supreme Court in 1976 allowed capital punishment to resume.

At issue is whether the New Orleans-based 5th U.S. Circuit Court of Appeals was correct when it refused attempts by Buck’s attorneys to reopen a judgment against Buck. That ruling blocked his lawyers from moving forward with an appeal contending Buck’s constitutional rights were violated when his defense lawyers put on an expert witness who referred to Buck’s race during his testimony.

In Texas death penalty trials, one of the “special issues” jurors must consider when deciding punishment is whether the defendant they’ve convicted would be a continuing future danger.

A psychologist, Dr. Walter Quijano, one of two defense experts hired by Buck’s lawyers for his 1997 trial, compiled a report listing race as among several statistical factors like age, sex and criminal past that influenced the probability Buck would commit a violent act in the future.

“It’s a sad commentary that minorities, Hispanics and black people, are over-represented in the criminal justice system,” Quijano testified, according to court records. He also said based on his interview and testing of Buck, the defendant was unlikely to commit future violent criminal acts although Quijano said he could “never rule out any probability.”

During the course of cross-examination, a Harris County prosecutor asked him once about race and sex being a factor in future dangerousness and Quijano replied, “Yes.” Defense attorneys submitted his report into evidence and over objection of prosecutors it was admitted. The prosecutor referred to Quijano during closing arguments to jurors but did not mention race.

Buck’s current lawyers contend his trial attorneys were deficient for using Quijano and for not objecting to his testimony during the cross-examination and that lawyers early in the appeals process were deficient for not raising the issue of trial attorney ineffectiveness.

The Texas Attorney General’s Office said in its brief to the justices that Quijano’s disputed testimony “played a very limited role, and Quijano’s ultimate conclusion was that (Buck) would likely not be a future danger.”

Buck’s case was among six in 2000 that then-Texas Attorney General John Cornyn, now a Republican U.S. senator, in a news release said needed to be reopened because of Quijano’s racially charged statements. In the other five cases, new punishment hearings were held and each convict again was sentenced to death. Buck’s lawyers contended the attorney general broke a promise by contesting his case, although the 5th Circuit said while that circumstance was “odd and factually unusual,” they could find nothing in the case record to indicate the state made an error or promised not to oppose any move to reopen the case.

Buck, now 53, was within a six-hour window scheduled for his lethal injection in 2011 when the justices issued a reprieve so they could consider his appeal for a review of arguments about the race-tinged testimony. The court ultimately refused, although Justice Sonia Sotomayor, joined by Justice Elena Kagan, said Buck had presented issues that “deserve encouragement to proceed further.” A new appeal went to the Supreme Court in 2014, and a full-blown review was denied.

Buck’s lawyers then returned to the federal courts with a civil procedure known as Rule 60b, which seeks relief from a judgment due to extraordinary circumstances. The 5th Circuit, noting there was “little guidance as to what constitutes ‘extraordinary circumstances,'” rejected the appeal a year ago as procedurally barred. The court added, however, that even if the issue had been raised properly, it would have been rejected because the race issue first was brought up by Buck’s own trial lawyers, making it “a classic example of the defense ‘opening the door’ for the prosecutor to pursue the subject.”

It’s that rejection now before the high court.

Testimony showed Buck in July 1995 went to the home of his ex-girlfriend, Debra Gardner, 32, about a week after breaking up with her, shot his stepsister, killed Kenneth Butler, 33, and hunted down and killed Gardner, who had fled outside. Buck tried to drive away in his car, but it wouldn’t start. He was arrested by police while trying to run away.

Buck at the time was on parole after serving about a year of a 10-year prison term for delivery of cocaine. He also had a previous conviction for unlawfully carrying a weapon.