Updated

Texas' highest criminal court on Wednesday rejected an appeal from a convicted killer in a Houston case where supporters contend his death sentence unfairly was based on race.

With three of the nine justices dissenting, the Texas Court of Criminal Appeals refused an appeal from condemned inmate Duane Buck, 50, who was convicted of capital murder and sent to death row for the slaying of his ex-girlfriend and a man at her Houston apartment in July 1995.

During the punishment phase of Buck's 1997 trial, a psychologist testifying for the defense said black people were more likely to commit violence.  Advocates for Buck, who is black, say that unfairly influenced the jury, is grounds for a new sentencing hearing and should have been pursued more vigorously by lawyers early in the appeals process.

The appeals court "failed to recognize that his death sentence is the unconstitutional product of racial discrimination," Buck's lead attorney Kate Black, Christina Swarns, director of the Criminal Justice Practice at the NAACP Legal Defense and Educational Fund, and Kathryn Kase, executive director of Texas Defender Service, which represents a number of Texas death row inmates, said in a statement.

"We are gravely disappointed," they said. "With today's decision, Texas has once again reneged on its promise to ensure that Mr. Buck would not be executed pursuant to a death sentence that was the unfair product of a prosecutorial appeal to racial bias and stereotype."

They said they would take the case to the U.S. Supreme Court.

In its brief ruling Wednesday, the appeals court said Buck's appeal application filed in March "failed to satisfy" legal requirements and dismissed it "as an abuse of the writ without considering the merits of the claims."

But Judge Elsa Alcala, writing a 17-page dissent joined by Judges Tom Price and Cheryl Johnson, said the court should have used its discretion to consider the merits of the appeal and return it to the trial court for review.

"The record in this case reveals a chronicle of inadequate representation at every stage of the proceedings, the integrity of which is further called into question by the admission of racist and inflammatory testimony from an expert witness at the punishment phase," she wrote. "No court has ever considered the merits of (Buck's) legitimate claims for post-conviction relief."

Buck's case was among six that then-Texas Attorney General John Cornyn, now a Republican U.S. senator, in 2000 said needed to be reopened because of racially charged statements made during the sentencing phase. In the other five cases, new punishment hearings were held -- and each convict was again sentenced to death.

In Texas, jurors must decide on the future danger of an offender when they are considering a death sentence.

The attorney general's office, arguing in appeals as Buck's scheduled September 2011 execution approached, said Buck's case was factually and legally different from the five others and that Buck's trial lawyers first elicited the testimony from the psychologist, who was a defense witness. They also said the racial reference was a small part of larger testimony about prison populations.

Buck was within a six-hour period set for his execution on Sept. 15, 2011, when the Supreme Court gave him a reprieve. The high court decided months later not to review his case and lifted its reprieve.

He does not currently have an execution date.

Buck was convicted of gunning down ex-girlfriend Debra Gardner, 32, and Kenneth Butler, 33, outside Houston on July, 30, 1995, a week after Buck and Gardner broke up. Buck's stepsister also was shot but survived.