WASHINGTON — (CNN) The Supreme Court heard arguments concerning the death penalty on Wednesday, for the first time since the issue bitterly divided the justices last term.

The justices grappled with sentencing requirements and jury instructions in consolidated cases from Kansas, involving a decision by the Kansas Supreme Court to overturn death sentences for crimes that Justice Samuel Alito said “rank as among the worst.”

Wednesday’s cases come at a time when there is renewed national interest in the fundamental questions about the death penalty, increased judicial skepticism and dramatically less applications across the country. Justices Stephen Breyer and Ruth Bader Ginsburg have urged the court to revisit the constitutionality of the death penalty, although Wednesday’s cases did not consider that issue.

Cassandra Stubbs, director of the ACLU Capital Punishment Project, noted the court has so far agreed to hear four death penalty cases this term.

“I think in general we will see this term that the Court is going to be very closely scrutinizing the procedural questions concerning its implementation,” she said.

Several of the justices seemed skeptical of the arguments put forth by lawyers representing the convicted murderers, who are challenging their death sentences.

One of the cases deals with two brothers, Reginald and Jonathan Carr, who went on a brutal crime spree in December of 2000 in Wichita, Kansas. It began when they carjacked and robbed a victim named Andrew Schreiber, forcing him at gunpoint to travel from ATM machines and make withdrawals from his bank account. Four days later, they attacked an orchestra cellist named Linda Ann Walenta who later died as a result of her injuries. Finally, three days later, they invaded the home of three victims and engaged in sex crimes, kidnappings and murders. In all there were four murders that night. One victim, identified in court papers as “Holly G.,” survived apparently because her hairclip deflected a bullet to the head.

The justices were clearly concerned with the gravity of the crime.

Justice Antonin Scalia read a summary of the crimes in open court.

Alito said that the Carr brothers were involved “in some of the most horrendous murders that I have seen in my 10 years here, and we see practically every death penalty case that comes up anywhere in the county.”

The brothers were convicted and sentenced to death. The Kansas Supreme Court however, reversed the death sentences.

The state’s high court noted that the Eighth Amendment requires individualized consideration of a defendant at capital sentencing hearings and said that the trial court violated the requirement when it allowed a joint penalty proceeding. The Kansas court found that the brothers needed separate penalty proceedings because the evidence supporting one brother’s sentence could be seen as antagonistic to the other.

Frederick Liu, a lawyer for Reginald, explained his why his client suffered from the joint hearing. He said, for instance, that one specialist testified that Jonathan, the younger brother, “Looked up to Reggie.”

“These are precisely the sort of evidence that shows that however bad you think Jonathan is, Reginald is worse,” he said. “It is in a sense making Reginald doubly culpable for these offenses.”

Alito questioned whether separate proceedings could further traumatize victims and waste resources.

“Do you think that the desire to spare Holly from having to testify more than once is a relevant factor here,” he asked.

And Breyer worried about “throwing a huge monkey wrench” into ordinary cases involving gangs and drugs where joint proceedings are very common and “reversal is very rare.”

Stephen R. McAllister, Solicitor General of Kansas, said the Kansas Supreme Court was wrong.

“The joint sentencing proceeding in these cases did not violate the Eighth Amendment,” he said, “because each defendant received the individualized sentencing determination to which he was entitled.”

Rachel P. Kovner, Assistant to the Solicitor General, argued for the Justice Department in support of Kansas.

“Joint proceedings can enhance accuracy and fairness as a long line of this Court’s cases hold,” she said.

Kovner told the justices that joint proceedings offer a “fuller evidentiary record” to juries and prevent “arbitrary disparities that may arise when two juries reach inconsistent conclusions about the common facts of a single crime.”

The justices also considered a technical question about whether a jury instruction for the penalty phase of the capital trial was consistent with the Eighth Amendment’s ban on cruel and unusual punishment. Lawyers for the Carr brothers as well as Sydney Gleason, a Kansas man convicted of murder, argued that the jury wasn’t allowed to properly consider so called “mitigating factors” that might justify a sentence of life without parole instead of death.

Neal K. Katyal, a lawyer for one of the brothers told the justices, said, “a man is being put to death under jury instructions that are so confusing that there is a reasonable likelihood that some juries would interpret those instructions to bar consideration of the mitigating circumstances and others would not.”

“That ambiguity and inequality is impermissible under the Eighth Amendment,” he said

But Kansas Attorney General Derek L. Schmidt said that the death sentences were fair. “Each of these jurors was able to give meaningful effect to anything and everything they heard,” he said.

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