WASHINGTON (CNS) -- The U.S. Supreme Court agreed June 6 to take on two very different death penalty cases from Texas in its next term.

The court, looking at specific angles of the death penalty, will examine potential racial bias influencing sentencing and the use of outdated standards in determining intellectual disabilities in capital cases.

Texas leads the nation in executions with 537 since 1976, nearly five times the number of any other state.

Karen Clifton, executive director of the Catholic Mobilizing Network in Washington, said she was pleased the court will consider the two cases.

"As the use of the death penalty continues to decline in our country, we are seeing this punishment is increasingly reserved for the most vulnerable: people of color, the poor and the intellectually disabled," she told Catholic News Service in a June 7 email.

She also noted that the death penalty's use is "isolated to a few geographic jurisdictions so it is no surprise these cases both come from the same state and the same county."

The court is by no means chipping away at the death penalty with these cases, said Meg Penrose, professor of constitutional law at Texas A&M University's School of Law, but she said the case about intellectual disabilities could influence other cases across the country while the issue of race influencing a death sentence absolutely must be examined.

Penrose said a key aspect of both cases is that if the outcome is a 4-4 vote, without a replacement for Justice Antonin Scalia, both men will be executed since the lower and appeals courts ruled against them and these decisions will stand.

The case of Buck v. Stephens, involves Duane Buck who was sentenced to death for 1995 murders of his ex-girlfriend and another man in front of her children in Houston in 1995. A psychologist who spoke at the punishment phase of his trial said that because Buck is African-American, there was a stronger likelihood that he could present a danger to society.

Although much attention has been given to this remark, Penrose noted that the case hangs on procedure and examines if that phase of his trial was ineffective because the witness was called forth by the defense.

If the court rules in Buck's favor, he will only get a new sentencing hearing, not a new trial establishing guilt or innocence.

The other Texas case up for review is Moore v. Texas, involving Bobby James Moore, who killed a grocery store clerk during a botched robbery in 1980. Moore claims to be intellectually disabled, a claim the state appeals court has rejected. However, his attorneys argue the state used outdated medical standards in their evaluation.

Moore's attorneys also argued that executing someone after so long on death row is unconstitutional, but the court will not look at that aspect of his sentence.

Both cases are decades old and prove one thing according to Penrose: "If society is going to inflict the ultimate penalty, it needs to be sure it has done so in a just manner."

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Follow Zimmermann on Twitter: @carolmaczim.