The Supreme Court dived into the internal workings of jury deliberations in capital cases Wednesday, debating whether jurors could have lingering doubts about a defendant's guilt after a conviction and whether they could find that evidence for and against the death penalty was evenly balanced.

Less than a week after the nation's 1,000th execution since states resumed capital punishment, the justices devoted their entire argument session to whether the Oregon and Kansas Supreme Courts had correctly interpreted the Eighth Amendment's prohibition on cruel and unusual punishment.

In both arguments, the justices struggled to understand the positions of attorneys for the death row inmates who wanted the high court to stay out of their cases -- and did little to support the rulings from the state courts that said the Constitution protects their clients.

"You win on the Eighth Amendment ... and when you leave the courthouse, you say, 'I don't want it anymore,"' an incredulous Chief Justice John Roberts told attorney Richard L. Wolf, who represents an Oregon death row inmate.

During the arguments in the Kansas case, Justice Antonin Scalia said jurors, in weighing all of the evidence, always have a way out: they can grant mercy to a defendant. "That clearly exists under (the Kansas) scheme ... What else do you have to do?" he asked of attorney Rebecca E. Woodman, who represents the Kansas inmate.

In the Oregon case, the justices were asked to decide whether a jury can consider "residual" or lingering doubts they have about a defendant's guilt in deciding whether to impose life in prison or the death penalty.

The state of Kansas also asked the high court to determine whether the Constitution bars states from allowing juries to impose a death sentence if they conclude that aggravating evidence of the crime's brutality and mitigating factors explaining a defendant's actions are equal in weight.

The cases are significant because they arise at a time when the court is undergoing one of its biggest shake-ups in decades. The court has a new chief and it is losing one of its most influential members -- Sandra Day O'Connor -- to retirement.

O'Connor has often been the swing vote in capital cases, including a 5-4 decision earlier this year that overturned a ruling against a Pennsylvania inmate by appeals court Judge Samuel Alito, President Bush's pick to replace O'Connor.

In 1972, the high court struck down the death penalty because of arbitrary sentencing procedures used by states. Four years later, justices said states could use the death penalty if they added safeguards to sentencing procedures.

But in recent years, O'Connor and other justices, including Ruth Bader Ginsburg and John Paul Stevens, have expressed concerns that capital defendants are not getting adequate legal representation. In August, Stevens told the American Bar Association that recent exonerations of death row inmates through DNA testing raise questions about the "wisdom" of continuing with capital punishment.

The first case argued Wednesday involves Randy Lee Guzek, who is on death row in Oregon for the June 1987 murders of Rod and Lois Houser, the uncle and aunt of Guzek's former high school girlfriend.

Guzek's murder convictions have been upheld by the state's highest court. But changes in Oregon law and mistakes by the trial judge led the Oregon Supreme Court to overturn his death sentence three times.

Yet another jury must decide Guzek's sentence. States -- including Oregon -- allow previous trial testimony to be used to educate jurors about the crime. The Oregon high court said Guzek can use alibi testimony from his grandfather and mother to impeach two co-defendants, who labeled Guzek as the leader in the double murder.

But Oregon Solicitor General Mary Williams argued that allowing Guzek to offer evidence of his innocence during the sentencing hearing is improper because it will force prosecutors to prove his guilt all over again.

The second case centered on Michael Lee Marsh, who was convicted in the June 1996 killings of Marry Ane Pusch and her 19-month-old daughter, M.P.

After hearing Marsh's appeal, the Kansas Supreme Court last year struck down the state's death penalty law, finding that it unconstitutionally directed jurors to impose capital punishment if they determined that the aggravating factors offered by the prosecution and the mitigating evidence touted by the defense were of equal weight.

The cases are Oregon v. Guzek, 04-928, and Kansas v. Marsh, 04-1170.